List of top Mathematics Questions on Differential Equations asked in CUET (UG)

The integrating factor of differential equation \(\frac{dy}{dx}+y=\frac{1+y}{x}\) is:

The sum of the order and degree of differential equation \(2x^3\left(\frac{d^2y}{dx^2}\right)^4 + \frac{d^3y}{dx^3}+y=0\) is :

The integrating factor of the differential equation (1 +y²)dx - (tan^-1 y - x)dy = 0, is :

If \(\frac{d}{dx}(2\frac{d^2y}{dx^2})^3= 7\), then the sum of order and degree of the differential equation is:

If \(y=log[\frac{x^2}{e^2}]\) then value of \(\frac{d^2y}{dx^2}\) is:

The differential equation whose solution is Ax²+By²=1 where A and B are arbitrary constant is of:
(A) first order and first degree
(B) second order and first degree
(C) second order and second degree
(D) second order
Choose the correct answer from the options given below:

Integrating factor of the differential equation \((1-y²) \frac{dx}{dy} + xy = ay\) is:

If \(x\sqrt{1+y}+y\sqrt{1+x}=0;x\ne y\), then the value of \(\frac{d^2y}{dx^2}+2\frac{dy}{dx}\) at x = 1 is :

Match List I with List II

List I	List II
\(A.\ [1 + (\frac{dy}{dx})^2] = \frac{d^2y}{dx^2}\)	I. order 2, degree 3
\(B. \ (\frac{d^3y}{dx^2})^2 - 3\frac{d^2y}{dx^2} + 2(\frac{dy}{dx})^4 = y^4\)	II. order 2, degree 1
\(C. \ (\frac{dy}{dx})^2 + (\frac{d^2y}{dx^2})^3 = 0\)	III. order 1, degree 2
\(D.\ (\frac{dy}{dx})^2 + 6y^3 = 0\)	IV. order 3, degree 2

Choose the correct answer from the options given below:

If \(y=sin^{-1}x \) and \((1-x^2)\frac{d^2y}{dx^2} -x \frac{dy}{dx}=K\),then value of K is:

The general solution of the differential equation $\frac{dy}{dx}+\frac{x}{y}=0$ is ________.

The solution of the differential equation $\frac{dx}{dy}+Px=Q$, where P and Q are constants or functions of y, is given by ________.