List of top Mathematics Questions on Differential equations asked in AP ECET BSc Mathematics

\[ \frac{1}{D^{3}-3D^{2}+4}\,e^{2x}=\_ \]

\[ \frac{1}{D-a}X=\_ \]

The differential equation corresponding to the general solution $y = c_{1} + (c_{2}x + c_{3})e^{2x}$ is}

Particular integral of $(D^{2} + D)y = x^{2} + 2x + 4$ is}

Particular integral of $y'' + y = \cosh 3x$ is

The complementary function of $y'' - 3y' + 2y = e^{3x}$ is}

Particular integral of $\frac{1}{(D - 2)^{2}} e^{2x} = $

The general solution of $x^{4}p^{2} = y + px$, $p = \frac{dy}{dx}$ is}

The general solution of $xp^{2} - 2yp + ax = 0$ is where $p = \frac{dy}{dx}$.

The general solution of $4xp^{2} = (3x - a)^{2}$, $p = \frac{dy}{dx}$, is}

The solution of $y = 2px + 4yp^{2}$ is}

Solution of $\frac{d^{2}y}{dx^{2}} + 4\frac{dy}{dx} + 29y = 0$, $y(0) = 0$ is}

Particular solution of $y'' + y = \cos x$ is

The differential equation $\frac{dy}{dx} = \frac{-(x + x^{8} + py^{2})}{y^{8} - y + qxy}$ is exact if}

The solution of $p = \tan(px - y)$ is (where $p = \frac{dy}{dx}$)

The solution of $y^{4}dx + 2xy^{3}dy = \frac{ydx - xdy}{x^{3}y^{3}}$ is}

Which of the following is an integrating factor of $(x^{2} + y^{2} + 2x)dx + 2ydy = 0$?

The integrating factor of $x \cos x \frac{dy}{dx} + (x \sin x + \cos x) y = 1$ is}

If $y = y(x)$ is the solution of $\left(\frac{2 + \sin x}{y + 1}\right) \frac{dy}{dx} + \cos x = 0$ with $y(0) = 1$, then $y\left(\frac{\pi}{2}\right) = $

The solution of \[ x\frac{dy}{dx}+y=x^4 \] with \[ y(1)=\frac{6}{5} \] is

Which of the following is the solution of \[ p^2+p\left(\frac{y}{x}-\frac{x}{y}\right)-1=0, \] where \[ p=\frac{dy}{dx}\,? \]

General solution of \[ y=x\left(p+\sqrt{1+p^2}\right) \] is \( \_\_\_\_ \), where \[ p=\frac{dy}{dx}. \]

Solution of \[ p^3y+2px-y=0 \] is \(____\), where \[ p=\frac{dy}{dx}. \]

General solution of \[ xp^2-yp+a=0, \] is \( \_\_\_\_ \), where \[ p=\frac{dy}{dx}. \]

The complementary function of \[ (D-2)^2y=8e^{-x} \] is