List of top Mathematics Questions on Differential equations asked in COMEDK UGET

The function \[ x+y=\tan^{-1}y \] is the solution of which of the following differential equations?

If $\dfrac{dy}{dx}=y\tan x$, then the solution of the differential equation is:

If the tangent at any point $(x,y)$ of a curve intercepts equal lengths on the coordinate axes, then the differential equation of the curve is:

Let the population of a species of birds surviving at a time \(t\) be governed by the differential equation \[ \frac{dp}{dt}-p=-100 \] If \(p(0)=50\), then \(p(-\ln2)\) is equal to:

Solution of the differential equation \( \frac{dy}{dx} + x = 0 \) represents a family of

Solve the following differential equation \( \cos^2 x \frac{dy}{dx} + y = \tan x \), given that \( y(0)=1 \). Hence find \( y\left(\frac{\pi}{4}\right) \)

The number of solutions of \( \frac{dy}{dx} = \frac{y+1}{x-1} \), when \( y(1) = 2 \) is:

The solution of the differential equation: \( x\cos y\,dy = (xe^x\log x + e^x)dx \) is

Integrating factor of the differential equation \[ \frac{dy}{dx} + y = \frac{x^3 + y}{x} \]

The solution of the differential equation \( \frac{dy}{dx}+y\log y\cot x=0 \) is

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

The solution of \( (x+\log y)dy+ydx=0 \) when \( y(0)=1 \) is