List of top Mathematics Questions on Differential equations asked in KEAM

The solution of the differential equation $(y+x^{2})dx=xdy, x>0$ is a curve which passes through the point (1,0). The equation of the curve is

Elimination of arbitrary constants $A$ and $B$ from $y = Ae^x + Be^{-2x}$ gives the differential equation:

The solution of the differential equation $(x + 2y)dx + (2x - y)dy = 0$ is

The general solution of the differential equation \((1 + y)dx - (1 - x)dy = 0\) is

The integrating factor of the differential equation \((1 + x^{2})dy = (1 - 2xy)dx\) is

The integrating factor of the differential equation \( \sin x\, dy = \frac{1}{2}(\sin2x + 2y\cos x)\,dx \) is

If \( y'(x) = 2y \), \( y(x) \ge 0 \) and \( y(0) = e^2 \), then \( y(x) = \)

The solution of the differential equation $\frac{dy}{dx} = \frac{y^2}{x}$ passing through the point $(1,-1)$ is

The differential equation which represents the family \( y^2 = 2c(x+\sqrt{c}) \) is

If \( \frac{dy}{dx} = \frac{2}{x+y} \) and \( y(1)=0 \), then \( x+y+2 \) equals

The solution of the differential equation \( 5y\,dx = 2x\,dy \) passing through the point \( (1,1) \) is:

The differential equation whose general solution is \( y = e^x(A\cos x + B\sin x) \) is

The differential equation whose general solution is \( y = e^x(A\cos x + B\sin x) \) is

The differential equation whose general solution is \( y = e^x(A\cos x + B\sin x) \) is

The solution of \( \frac{dy}{dx} + y \tan x = \sec x \), given \( y(0) = 0 \), is:

The general solution of the differential equation $(x + y + 3)\frac{dy}{dx} = 1$ is:

The general solution of the differential equation $x \, dy - y \, dx = y^2 \, dx$ is:

The solution of the differential equation \( y'(y^2 - x) = y \) is

The slope of a curve at any point \((x,y)\), other than origin, is \( y + \frac{y}{x} \). Then the equation of the curve is

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

The value of the integral \( \int_{2}^{4} \left( \frac{\log t}{t} \right) \, dt \) is equal to:

The solution of the differential equation \( (kx - y^2) dy = (x^2 - ky) dx \) is:

The value of the integral \( \int_{2}^{4} \left( \frac{\log t}{t} \right) \, dt \) is equal to:

The solution of the differential equation \( (kx - y^2) dy = (x^2 - ky) dx \) is:

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