Question 1 :
The degree and order of $D.E$ of the family of rectangular hyperbola whose axes are symmetry to the co-ordinate axes are
Question 2 :
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 3 :
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 4 :
The number of arbitrary constants in the particular solution of a differential equation of third order are:
Question 5 :
Consider a differential equation of order $m$ and degree $n$. Which one of the following pairs is <i>not</i> feasible?
Question 6 :
Identify the order of the $ln (ay) = be^{x} + c$, (where $a, b, c$ are parameters)
Question 7 :
The differential equation for all the straight lines which are at a unit distance from the origin is
Question 8 :
The solution of, $\dfrac{xdy}{x^2 + y^2} = \left(\dfrac{y}{x^2 + y^2} - 1 \right)dx$, is given by
Question 9 :
The order and degree of the differential equation $\sqrt { \dfrac { dy }{ dx } } -4\dfrac { dy }{ dx } -7x=0$ are
Question 10 :
The solution of the differential equation $\left( 1+y^{ { 2 } } \right) +\left( x-e^{ { { \tan }^{ -1 }y } } \right) \dfrac { dy }{ dx } =0,$ is
Question 11 :
Degree and order of the differential equation $\dfrac { { d }^{ 2 }y }{ d{ x }^{ 2 } } ={ \left( \dfrac { dy }{ dx } \right) }^{ 2 }$ are respectively
Question 12 :
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 13 :
What is the general solution of the differential equation $x\, dy - y\, dx \,y^2$ ?
Question 14 :
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 15 :
What is the solution of the differential equation $\sin \left (\dfrac {dy}{dx}\right ) - a = 0$?<br>where $c$ is an arbitrary constant.
Question 16 :
For $y = \cos (m \sin^{-1} x)$ which of the following is true?
Question 18 :
The order and degree of the differential equation $(y''')^2 + (y'')^3 - (y')^4 + y^5 = 0$ is
Question 19 :
The differential equation of the simple harmonic motion given by $x=A\cos { \left( nt+\alpha \right) } $ is
Question 20 :
Which of the following is true about this equation: $(xy+2) \left(\dfrac{dy}{dx}\right)^3+\left(\dfrac{dy}{dx}\right)^2+5x^2=0$
Question 21 :
What is the order of the differential equation ${ \left( \dfrac { dy }{ dx }  \right)  }^{ 2 }+\dfrac { dy }{ dx } -\sin ^{ 2 }{ y } =0$.
Question 22 :
The differential equation representing the family of curves $y^{2}=2c\left ( x+\sqrt{c} \right )$, where $c> 0$, is a parameter, is of order and degree as follows:<br/>
Question 24 :
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 $?
Question 25 :
State the order and degree of the given differential equation, if the order is a and degree is b, find a+b?<br/>$\dfrac{d^{2}y}{dx^{2}}=\left [ 1+\left ( \dfrac{dy}{dx} \right )^{2} \right ]^{3/2}$.<br/><br/>
Question 26 :
Eliminating the arbitrary constants B and C in the expression $y=\displaystyle\frac{2}{3C}(Cx-1)^{3/2}+B$, we get.
Question 27 :
The order of the differential equation of all parabolas, whose latus rectum is $4a$ and axis parallel to the x-axis, is
Question 28 :
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 29 :
The order and degree of the differential equation of the family of the circles touching the $x$-axis at the origin, are respectively:
Question 30 :
The order and degree of the differential equation $y' + (y'')^2 = (x+y'')^2$ are:
Question 31 :
$\cfrac { d }{ dx } \left[ \tan ^{ -1 }{ \cfrac { \sqrt { 1+{ x }^{ 2 } } -1 }{ x } } \right] $ is equal to
Question 33 :
The order of the differential equation whose solution is $y=a\cos { x } +b\sin { x } +c{ e }^{ -x }$, is
Question 34 :
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 35 :
The solution of differential equation $x\cos^{2}y dx = y\cos^{2} x  dy$ is
Question 36 :
The degree of the differential equation of all curves having normal of constant length $c$ is:<br/><br/>
Question 37 :
The order and degree of the differential equation ${ y }^{ 2 }=4a(x-a)$, where $a$ is an arbitrary constant, are respectively
Question 38 :
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 41 :
The different equation of the family of parabolas with focus at origin and x-axis as axis is
Question 43 :
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 45 :
Consider the function $\mathrm{f}:(-\infty, \infty)\rightarrow(-\infty, \infty)$ defined by $\displaystyle \mathrm{f}(\mathrm{x})=\frac{\mathrm{x}^{2}-\mathrm{a}\mathrm{x}+1}{\mathrm{x}^{2}+\mathrm{a}\mathrm{x}+1}$ , $0<\mathrm{a}<2$.<br/>Which of the following is true?<br/>
