Question 1 : What is the general solution of the differential equation $x\, dy - y\, dx \,y^2$ ?

Question 3 : Solution of the different equation, $ydx - xdy + x{y^2}dx = 0$ can be.

Question 4 : The solution of the differential equation $\left( 1+y^{ { 2 } } \right) +\left( x-e^{ { { \tan }^{ -1 }y } } \right) \dfrac { dy }{ dx } =0,$ is

Question 5 : The degree of $\dfrac{d^2 y}{dx^2} + \left[1 + \left(\dfrac{dy}{dx} \right)^2 \right]^{3/2} = 0$ is

Question 6 : The solution of, $\dfrac{xdy}{x^2 + y^2} = \left(\dfrac{y}{x^2 + y^2} - 1 \right)dx$, is given by

Question 7 : The degree of the differential equation $\displaystyle \sqrt[3]{1 + \left( \dfrac{dy}{dx} \right )^{\tfrac{1}{2}}} = \dfrac{d^2y}{dx^2}$ is:

Question 8 : The population $p(t)$ at time $t$ of a certain mouse speciessatisfies the differential equation $\dfrac { d p ( t )} { d t } = 0.5 p ( t ) - 450.$If $p ( 0 ) = 850 ,$ then the time at which the population becomes zero is

Question 9 : The order, degree of the differential equation satisfying the relation $\sqrt{1+x^{2}}+\sqrt{1+y^{2}}=\lambda (x\sqrt{1+y^{2}})-y\sqrt1+x^{2})$ is

Question 11 : What is the solution of the differential&#160;equation $\dfrac{dy}{dx} +\dfrac{y}{x} = 0 $ ?<br/>Where c is a constant.

Question 12 : Consider a differential equation of order $m$ and degree $n$. Which one of the following pairs is <i>not</i> feasible?

Question 14 : Which one of the following is the differential equation that represents the family of curves $ y = \dfrac{1}{2x^2 - c}$ where c is an arbitrary constant ?

Question 15 : Consider the differential equation $y = px + \sqrt{a^2 p^2 + b^2}$,where $p =\dfrac{dy}{dx}$. The order and degree of the differential equation are

Question 16 : The order and degree of the differential equation $\sqrt { \dfrac { dy }{ dx } } -4\dfrac { dy }{ dx } -7x=0$ are

Question 17 : Identify the order of the&#160;$ln (ay) = be^{x} + c$, (where $a, b, c$ are parameters)

Question 18 : What is the solution of the differential equation $\dfrac {dx}{dy} + \dfrac {x}{y} - y^{2} = 0$?<br>where $c$ is an arbitrary constant.

Question 20 : Degree and order of the differential equation $\dfrac { { d }^{ 2 }y }{ d{ x }^{ 2 } } ={ \left( \dfrac { dy }{ dx } \right) }^{ 2 }$ are respectively

Question 21 : $y = \sin kt$ satisfies the differential equation $y'' + 9y = 0$. Then $k=$<br/>

Question 22 : The number of arbitrary constants in the particular solution of a differential equation of third order are:

Question 23 : The degree of the differential equation $\left[ 1 + \left( \dfrac{dy}{dx} \right )^2 \right ]^{2} = \dfrac{d^2 y}{dx^2}$ is:

Question 24 : The order of the differential equation of the parabola&#160;whose axis is parallel to y-axis is:

Question 25 : Consider the following statements in respect of the differential equation$\frac{d^2y}{dx^2}+cos \left ( \frac{dy}{dx} \right )=0 :$<br>1. The degree of the differential equation is not defined. <br>2. The order of the differential equation is 2.<br>Which of the above statements is/are correct ?

Question 27 : The differential equation for all the straight lines which are at a unit distance from the origin is

Question 28 : The degree and the order of the differential equation $y=x{ \left( \cfrac { dy }{ dx } &#160;\right) &#160;}^{ 2 }+{ \left( \cfrac { dx }{ dy } &#160;\right) &#160;}^{ 2 }$ are respectively:

Question 29 : The differential equation&#160;$1 + \dfrac{{dy}}{{dx}} - {\left( {\dfrac{{{d^2}y}}{{d{x^2}}}} \right)^{3/2}} = 0$ is of

Question 30 : The degree and order of $D.E$ of the family of rectangular hyperbola whose axes are symmetry to the co-ordinate axes are

Question 31 : Order and degree of the differential equation $\left [1 + \left (\dfrac {dy}{dx}\right )^{3}\right ]^{\tfrac {7}{3}} = 7 \dfrac {d^{2}y}{dx^{2}}$ are respectively:<br/>

Question 32 : What is the solution of the differential equation $\sin \left (\dfrac {dy}{dx}\right ) - a = 0$?<br>where $c$ is an arbitrary constant.

Question 33 : If $dy=x^2dx$,&#160;what is the equation of $y$ in terms of $x$ if the curve passes through $(1,1)$?<br/>

Question 34 : The D.E.&#160; of the family of straight lines $y= mx +\frac{a}{m}$ where m is the parameter is&#160;

Question 35 : The number of arbitrary constants in the general solution of a differential equation of fourth order are

Question 36 : The differential equation representing the family of curves $\mathrm{y}^{2}=2\mathrm{c}(\mathrm{x}+\sqrt{\mathrm{c}})$, where $\mathrm{c} &gt;0$, is a parameter, is of order and degree as follows:&#160;<br/>

Question 38 : If $ x\dfrac{dy}{dx} = y(\log y - \log x + 1) $, then the solution of the equation is

Question 39 : Solution of $(x + y)^{2} \dfrac {dy}{dx} = a^{2} ('a'$ being a constant) is:

Question 40 : The order and degree of the differential equation $\left [1 + \left (\dfrac {dy}{dx}\right )^{2} \right ]^{3} = \rho^{2} \left [\dfrac {d^{2}y}{dx^{2}}\right ]^{2}$ are respectively.

Question 41 : The differential equation which represents the family of curves $y = c_1e^{c_2x}$, where $c_1 $ and $ c_2$ are arbitrary constants, is

Question 42 : What is the order of the differential equation ${ \left( \dfrac { dy }{ dx } &#160;\right) &#160;}^{ 2 }+\dfrac { dy }{ dx } -\sin ^{ 2 }{ y } =0$.

Question 44 : The order and degree of D.E $\left [ 1+\dfrac{d^{3}y}{dx^{3}} \right ]^{1/3}=\dfrac{d^{2}y}{dx^{2}}$ is:

Question 45 : The degree of D.E $\left [ 5+\left ( \dfrac{dy}{dx} \right ) ^{2}\right ]^{5/3}=7\left ( \dfrac{d^{2}y}{dx^{2}} \right )$

Question 46 : The degree and order of the differential equation of the family of all parabolas whose axis is the $x$-axis, are respectively:

Question 47 : $y = 2\cos { x } +3\sin { x }$ satisfies which of the following differential equations?<br>1. $\dfrac { { d }^{ 2 }y }{ d{ x }^{ 2 } } +y=0$<br>2. ${ \left( \dfrac { dy }{ dx } \right) }^{ 2 }+\dfrac { dy }{ dx } =0$<br>Select the correct answer using the code given below.

Question 49 : What is the equation of a curve passing through (0, 1) and whose differential equation is given by dy = y tan x dx ?<br>

Question 50 : The solution of the equation $ (x^{2}y + x^{2})dx + y^{2}(x-1)dy = 0 $ is given by

Question 51 : The order and degree of the differential equation of the family of the circles touching the $x$-axis at the origin, are respectively:

Question 52 : The degree of the differential equation of all&#160;curves having normal of constant length $c$ is:

Question 54 : The solution of the differential equation $2x \dfrac{dy}{dx} = y; y(1) = 2$ represents $=$ ____.

Question 55 : Solution of the differential equation $\tan{y}\sec ^{ 2 }{ x } dx+\tan { x } \sec ^{ 2 }{ y } dy=0$ is:

Question 56 : Find the degree of&#160;$\left [ 1+\left ( \cfrac{d^{2}y}{dx^{2}} \right )^{2} \right ]=\left [ 2+\left ( \cfrac{dy}{dx} \right )^{2} \right ]^{3/2}$&#160;

Question 61 : Order of&#160;$\left ( \dfrac{dy}{dx} \right )^{3}+\left ( \dfrac{dy}{dx} \right )^{2}+y^{4}=0$ is:

Question 62 : What are the order and degree, respectively, of the differential equation<br>${ \left( \cfrac { { d }^{ 3 }y }{ d{ x }^{ 3 } } \right) }^{ 2 }={ y }^{ 4 }+{ \left( \cfrac { dy }{ dx } \right) }^{ 5 }\quad $?

Question 63 : The differential equation of all conics with centreat origin is of order

Question 66 : The solution of the differential equation $ \dfrac{x+\dfrac{x^3}{3!}+\dfrac{x^5}{5!}+ \dots}{1+\dfrac{x^2}{2!}+\dfrac{x^4}{4!}+\dots}=\dfrac{dx-dy}{dx+dy} $ is

Question 67 : Degree of the differential equation $(y'')^2 - \sqrt{y'} = y^3$ is:

Question 68 : The order and degree of the differential equation $\dfrac{d^{2}y}{dx^{2}}=sin\left (\dfrac{dy}{dx}\right )+xy$ are:

Question 69 : If $\cos { x } \cfrac { dy }{ dx } -y\sin { x } =6x,(0&lt;x&lt;\cfrac { \pi }{ 2 } )$ and $\quad y\left( \cfrac { \pi }{ 3 } \right) =0\quad $ then $y\left( \cfrac { \pi }{ 6 } \right) $ is equal to:

Question 70 : The solution of differential equation $x \dfrac {dy}{dx} + y=y^2$ is:

Question 71 : If the general solution of some differential equation is $y={ a }_{ 1 }({ a }_{ 2 }+{ a }_{ 3 }).\cos { \left( x+{ a }_{ 4 } \right) } -{ a }_{ 5 }{ e }^{ x+{ a }_{ 6 } }\quad $ then order of differential equation is ____

Question 73 : Assertion: The order of the differential equation of all conics whose centre lies at $(0, 0)$ is $3$. Reason: The order of differential equation.is same as the number of arbitrary unknowns (constants) in the given curve.

Question 74 : The number of arbitrary constants in the solutionof a differential equation of degree 2 and order<b></b>3 is

Question 75 : The degree and order of the differential equation of the family of all parabolas whose axis is x-axis are respectively:

Question 76 : The order and degree of the differential equation $\displaystyle x^2=\frac{\left(1+\left(\frac{dy}{dx}\right)^2\right)^{3/2}}{\frac{d^2y}{dx^2}}$ are respectively :

Question 77 : The order and degree of the differential equation $\left ( 1\, +\, 3\, \displaystyle \frac {dy}{dx} \right )^{2/3}\, =\, 4\,&#160;\displaystyle \frac {d^3y}{dx^3}$ are:

Question 79 : What is the general solution of the differential equation ${ e }^{ x }\tan { y } dx+\left( 1-{ e }^{ x } \right) \sec ^{ 2 }{ y } dy=0$?

Question 80 : The differential equation by eliminating $A$ and $B$ from $y = Ax^3 + Bx^2$ is

Question 82 : If m and n are the order and degree of the differential equation $\displaystyle\left(\displaystyle\frac{d^2y}{dx^2}\right)^5+4\displaystyle\frac{\displaystyle\left(\frac{d^2y}{dx^2}\right)^3}{\displaystyle\frac{d^3y}{dx^3}}+\frac{d^3y}{dx^3}=x^2-1$, then

Question 83 : The value of the constant $'m'$ and $'c'$ for which $y=mx+c$ is a solution of the differential equation $D^2y-3Dy-4y=-4x$.

Question 84 : Assertion: The order of the differential equation whose solution is $y=c_{1}e^{2x+c_{2}}+c_{3}e^{2x+c_{4}}$ is 4. Reason: Order of the differential equation is the order of the highest order derivative occurring in the differential equation.

Question 88 : The order of the differential equation whose general solution is given by<br>$y=\left( { C }_{ 1 }+{ C }_{ 2 } \right) \sin { \left( x+{ C }_{ 3 } \right) } -{ C }_{ 4 }{ e }^{ x+{ C }_{ 5 } }$ is

Question 89 : The solution of the differential equation $\operatorname { xdy } \left( y ^ { 2 } e ^ { x y } + e ^ { \tfrac { x } { y } } \right) = y d x \left( e ^ { \frac { x } { y } } - y ^ { 2 } e ^ { x y } \right)$ is-

Question 90 : The order and degree of the differential equation ${ y }^{ 2 }=4a(x-a)$, where $a$ is an arbitrary constant, are respectively

Question 91 : lf $f (x)$ and $g (x)$ are two solutions of the differential equation $a\displaystyle \frac{\mathrm{d}^{2}\mathrm{y}}{\mathrm{d}\mathrm{x}^{2}}+\mathrm{x}^{2}\displaystyle\frac{\mathrm{d}\mathrm{y}}{\mathrm{d}\mathrm{x}}+\mathrm{y}=\mathrm{e}^{\displaystyle\mathrm{x}}$, then $f (x) - g (x)$ is the solution of<br>

Question 92 : $\cfrac { d }{ dx } \left[ \tan ^{ -1 }{ \cfrac { \sqrt { 1+{ x }^{ 2 } } -1 }{ x } } \right] $ is equal to

Question 94 : The different equation of the family of parabolas with focus at origin and x-axis as axis is

Question 95 : Consider the function $\mathrm{f}:(-\infty, \infty)\rightarrow(-\infty, \infty)$ defined by $\displaystyle \mathrm{f}(\mathrm{x})=\frac{\mathrm{x}^{2}-\mathrm{a}\mathrm{x}+1}{\mathrm{x}^{2}+\mathrm{a}\mathrm{x}+1}$ , $0&lt;\mathrm{a}&lt;2$.<br/>Which of the following is true?<br/>

Question 96 : The order of the differential equation whose solution is $y=a\cos { x } +b\sin { x } +c{ e }^{ -x }$, is

Question 97 : The differential equation of all vertical lines in a plane is?

Question 98 : The solution of differential equation $x\cos^{2}y dx = y\cos^{2} x &#160;dy$ is

Question 100 : The degree of the differential equation of all curves having normal of constant length $c$ is:<br/><br/>