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PROBLEMS ON DIFFERENTIAL EQUATION, 1) The degree of the differential equation (, , ), , ( ), , is …………………., 1), , not defined, , 2) The order of the differential equation, is ………………, 1), , not defined, , 3) The degree of the differential equation (, (, , ), , ) is ……….., 4, , 4) The degree of the differential equation, , ( ), , ) is …………, , 1), not defined, 5) The order and degree of the differential equation, [, , ( ) ], , ( ) can be solved by making the substitution …….., 1), 13) Which of the following is a homogeneous differential, equation?, (, 1) (, (, 2), 3) (, (, 4), 14) The solution of the differential equation, , 1), , (, , 12) A homogeneous differential equation of the form, , represents a family of …………., 1) straight lines 2) circles 3) parabolas, 15) The solution of the differential equation, 1), , 2), , 3), , 4), , is …………., , 1), 1), 4, 2, 6) The number of arbitrary constants in the general solution 17) The solution of the differential equation, of a differential equation of fourth order is …………., is ……………, 1), 0, 1), 2), 3), 7) The number of arbitrary constants in the particular, 18) The solution of the differential equation, solution of a differential equation of third order is …………., represents ……………., 1), 0, 1) a rectangular hyperbola, 8) The general solution of the differential equation, 2) parabola whose vertex is origin, is ……………, 3) straight line passing through origin, 1), 2), 4) a circle whose centre is at origin., 3), 4), 9) The order of the differential equation of all circles of given 19) The solution of the differential equation, is ……………., radius ‘a’ is ………………., 1), 1), 1, , 1), 11) Which of the following differential equation has, as one of its particular solution…………….., 1), , 0 is …., , 16) The solution of the differential equation ( ), , respectively are ……….., , 10) Which of the following differential equation has, as the general solution ……………., , 4) ellipses, , 4), , 3), 20) Which of the following is a second order differential, equation?, 1) (, 2), (, 3), 4), 21) The solution of the differential equation, 1), 3) t, , (, , 2), 4), , is ……, , (, , 3), GANESH HEGDE

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2, 22) Family, of curves is represented by the, differential equation of degree …………………, 1) 1, 2) 2, 3) 3, 4) 4, 23) The solution of the differential equation, is ………………, 1), , 2), , 3), , 4), , 33) The integrating factor of the differential equation, (, 1) √, , 4), , 34) The integrating factor of the differential equation, 1), 35) The integrating factor of, 1), , is ………….., 1), , 2), , 3), , 4), , 1), 26) The general solution of the differential equation of the, ∫(, , ∫, , 2), , ∫, , ∫(, , ∫, , is ………………, , 3), , 37), , 4), satisfies which of the following, differential equation …………….., 1), 3), , …………….., ∫, , 3), , 1), , is ……………….., , 1), , 2), , is ……………, , 36) The general solution of, , 25) The general solution of the differential equation, , type, , (, , is …………….., , 24) The solution of the differential equation, , 38) The differential equation of the family of curves,, where a is an arbitrary constant is …, , ∫, , ∫, ∫(, ∫, 4) ∫, ∫(, 27) The integrating factor of the differential equation, , 3), , is ……………, , is ……………, , 1) (, , (, , 3) (, , 4) (, , 39) The differential equation for which, is ……………, 1), , 1), 28) The integrating factor of the differential equation, (, , (, 1), , √, , 2), , √, , is …………, 3), , is ………….., , (, , 4), , (, , 40) Which of the following is the general solution of, …………, , 4), , 29) The general solution of the differential equation, (, is ………….., 1), 2), 3), 4), 30) The integrating factor of the differential equation, (, , 3), , (, (, 1), 2), 3), 4), 41) The general solution of the differential equation, is …………….., 1) y=c, , 2) y=c, , 3) y=(, 4) y=(, 1), 2), 3) g(, 42) The solution of the equation (, 31) Which of the following is not a homogeneous function of, (, is …………, x and y ………….., 1), 2), 3), 4), 1), ( ) 4), (, 43) Solution of, is give by …………, 32) The integrating factor of, is ………….., 1), 2), 3), GANESH HEGDE

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3, when (, , 44) The number of solution of, none, , PRACTICE PROBLEMS, is ….., 56) The degree of the differential equation (, , 2) one, , 3) two, 4) infinite, 45), is the general solution of the, differential equation …………….., 2) (, , 2) family of parabolas, 4) family of circles, , 1) 4, is ….., , 3), (, , is ……………, , (, (, 3), 4), 49) The differential equation for, where A and B are arbitrary constant is …………, , ( ) ], , ⁄, , 2), , 3) 2, , 4) not defined, , 58) The order and degree of the differential equation, ( ), , ⁄, , ⁄, , respectively are ………….., , 3), , ] then y is a solution of …….., , 3), , 4), , 51) The solution of the differential equation, is ………….., 3), 52) The elimination of A and B from the equation, gives the differential equation of order ……, 53) The solution of, , is …………….., 2), 4), , ( ), , is ……………., 1) 1, 2) 2, 3) 3, 4) 5, 60) The order and degree of the differential equation, ( ) ], , 1) 3, 4, , 4), [, , 59) The degree of the differential equation, , [, , 2), , 3), , 4) not defined, , 1) 2 and not defined 2) 2 and 2 3) 2 and 3 4) 3 and 3, , 48) The solution of, , 50) If, , 3) 3, , is ………………, , represents ………., , family of hyperbolas, 3) family of ellipses, 47) The general solution of, , 2) 2, , 57) The degree of the differential equation [, , (, , 46) The differential equation, , ( ) is ………….., , 1) 1, , (, , 4) (, , 3), , ( ), , ), , are ……………, 2)2,, , 3) 2, 1, , 4) 2, 3, , 61) Family, of curves will corresponds to a, differential equation of order …………………, 1) 1, 2) 2, 3) 3, 4) not defined, 62) The curve for which the slope of the tangent at any, point is equal to the ratio of the abscissa to the, rdi te f the p i t is ……………, 1) an ellipse, 2) a parabola, 3) a circle, 4) a rectangular hyperbola, 63) If m and n are the order and degree of the differential, equation (, , ), , (, , ), , (, , ), , then …………, , 1) m=3, n=1, 2) m=3, n=3, 3) m=3, n=2, 4) m=3, n=5, 64) Which of the following function is a solution of the, , differential equation ( ), ……………, 54) The differential equation obtained by eliminating A and B, from, is ……………., 1), 3), 2), 65) The differential equation of the family of curves, 3), 4), (, is ……………, 55) Solution of the differential equation, is ……., 1), (, ), 2), (, (, (, 3), 3), ( ), 4), ( ), GANESH HEGDE

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4, 66) General solution of, , is ………….., , 3), 67) The general solution of the differential equation, (, (, is ……………, (, (, 2) (, { (, , 3), , } 4), , (, , {, , 68) The solution of the differential equation, is ………………, 2), 3), , 4), , 69) The solution of the differential equation, is ………….., , (, , (, 2), (, 3), (, 4), 70) The general solution of the differential equation, (, |, 3), , |, , |, |, , is ………….., 2), , |, , 4), , |, , |, |, , }