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

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

If the slope of the tangent at a point $(x,y)$ on a curve is $\frac{y-4}{x}$ and the curve passes through $(4,3)$, then the point where it cuts the line $y=x$ is

The general solution of the differential equation: $$ \cos^2 x \cdot \frac{dy}{dx} + y = \tan x $$ is $$ y = \tan x - 1 + C e^{-\tan x} $$ If this solution satisfies $ y\left(\frac{\pi}{4}\right) = 1 $, then find $ C $.

The derivative of the function $f(x) = \sin(x^2)$ at $x = \sqrt{\pi}$ is

The integrating factor of the linear differential equation $\frac{dy}{dx} + P(x)y = Q(x)$ is a solution of the differential equation

By multiplying with $e^{\int P dx}$ on both sides of the equation $\frac{dy}{dx} + P(x)y = Q(x)$, the left side of the equation takes the form $\frac{d}{dx} (y f(x))$, then $f(x) =$