List of top Mathematics Questions on Differential equations asked in KEAM

The integrating factor of the differential equation \(\frac{dy}{dx} + \frac{2y}{20 - x} = 10\) is

If the solution of the differential equation \(\frac{dy}{dx} = \frac{\alpha x^2 + 4x - 4}{2y - 4}\), when \(y(1) = 3\), is \(y^2 - 4y = x^3 + 2x^2 - 4x + c\), then the value of \(\alpha\) is equal to

The integrating factor of the differential equation $2dy = (y + \cos x) dx$ is

The general solution of the differential equation $x^3 \frac{dy}{dx} + 3x^2 y = \cos x$ is

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 integrating factor of the differential equation $\frac{dy}{dx}-2y=2x-3$ is ________.

The solution of the linear differential equation \( \dfrac{dy}{dx}+y=e^{-x} \), when \( x=0,\ y=1 \), is

The general solution of the differential equation \( y\,dx-x\,dy=y^2(x\,dy+y\,dx) \) 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 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 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