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
The sum of the degree and order of the following differential equation \[ \left( 1 - \left( \frac{dy}{dx} \right)^2 \right)^{\frac{3}{2}} = kx \frac{d^2y}{dx^2} \] is
The solution of the differential equation \[ \frac{dy}{dx} + y \cos x = \frac{1}{2} \sin 2x \] is
The general solution of the differential equation \[ (1 + y^2) \, dx = ( \tan^{-1} y - x ) \, dy \] is:
The particular solution of \( e^{\frac{dy}{dx}} = 2x + 1 \) given that \( y = 1 \) when \( x = 0 \) is:
The solution of the differential equation $ \frac{dy}{dx} \tan y = \sin(x + y) + \sin(x - y) $ is
The general solution of $ \left( \frac{dy}{dx} \right)^2 = 1 - x^2 - y^2 + x^2y^2 $ is
The differential equation of all non-vertical lines in a plane is
The solution of the differential equation \( \sec^2 x \, \tan y \, dx + \sec y \, \tan x \, dy = 0 \) is:
The solution of the differential equation \[ y \frac{dy}{dx} = x \left[ \frac{y^2}{x^2} + \varphi \left( \frac{y^2}{x^2} \right) \right] \] is:
The solution of the differential equation \[ (1 + y^2) + (x - e^{\tan^{-1} y}) \frac{dy}{dx} = 0 \] is:
At present, a firm is manufacturing $1000$ items. It is estimated that the rate of change of production $P$ with respect to additional number of workers $x$ is given by $\frac {dP}{dx}=100-12 \sqrt x$ If the firm employees $25$ more workers, then the new level of production of items is
The solution of the differential equation $\frac{dy}{dx} = (x +y)^2$ is
A particular solution of $ \frac{dy}{dx} = (x+9y)^2$ when $ x = 0, y = \frac{1}{27}$ is