List of top Mathematics Questions on Differential equations asked in AP EAPCET

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

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

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

If the solution of \(\dfrac{dy}{dx}=\dfrac{y^3\cos\sqrt{x}}{\sqrt{x}e^{1/y^2}}\), \(y(0)=1\), is \(\dfrac{1}{y^2}=\log_e(f(x))\), then \(f(x)=\)

Suppose that \(f(x,y)\) and \(g(x,y)\) are homogeneous functions of same order. If \(x=Vy\) reduces the equation \(\dfrac{dy}{dx}=\dfrac{f(x,y)}{g(x,y)}\) to the form \(\dfrac{dV}{dy}=\dfrac{1}{y}(F(V))\), then \(F(V)=\)

The general solution of \(xdy-ydx=xy\,dy\) is