List of practice Questions

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

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

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 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 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 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 integrating factor of the differential equation $2dy = (y + \cos x) dx$ is

The general solution of the differential equation $x^3 \frac{dy}{dx} + 3x^2 y = \cos x$ is

If the solution of the differential equation \(\frac{dy}{dx} = \frac{\alpha x^2 + 4x - 4}{2y - 4}\), when \(y(1) = 3\), is \(y^2 - 4y = x^3 + 2x^2 - 4x + c\), then the value of \(\alpha\) is equal to

The integrating factor of the differential equation \(\frac{dy}{dx} + \frac{2y}{20 - x} = 10\) is

Differential equation for family \(y=ae^{2x}+bx^2\) is

If \(y=f(x)\) satisfies \[ \tan x \frac{dy}{dx}+(1+\tan^2 x)y=\tan x(1+\tan^2 x)^2 \] and passes through \(\left(\frac{\pi}{4},\frac{3}{4}\right)\), find \(f\left(\frac{\pi}{3}\right)\)