List of top Mathematics Questions on Differential Equations asked in AP PGECET

A function $y(x)$ such that $y(0) = 1$ and $y(1) = 4e$ is a solution of the differential equation $\frac{d^2y}{dx^2} - 2\frac{dy}{dx} + y = 0$. Then, $y(2)$ is equal to _______}

If $y(x) = C_1 \cos 2x + C_2 \sin 2x + A(x) \log (\sec 2x + \tan 2x)$ is the general solution of the differential equation $\frac{d^2y}{dx^2} + 4y = \tan 2x$, then $A(x) = \_\_\_\_\_\_\_$}

Consider the ordinary differential equation \[ x^2 \frac{d^2y}{dx^2} - 2x \frac{dy}{dx} + 2y = 0 \] with \( y(x) \) as a general solution. Given the values of \( y(1) = 1 \), \( y(2) = 5 \), the value of \( y(3) \) is equal to ______

The solution of the differential equation
\[ (D^3 - 5D^2 + 7D - 3)y = e^{-2x} \] is:

The given differential equation
$(x y^2 + n x^2 y) dx + (x^3 + x^2 y) dy = 0$ is exact when $n =$

The particular integral of the differential equation
\[ \frac{d^2y}{dx^2} - 6 \frac{dy}{dx} + 9y = e^{3x} \text{ is ............} \]

The general solution of the differential equation \( x^2 y'' - xy' + 5y = 0 \) is _______

Convert the non-linear equation \( xy' + y = x^4 y^3 \) into a linear one using the transformation \( z = y^{-2} \).
The linear equation is ...........

If \( \sin x \) is a solution of the differential equation \[ \dfrac{d^4 y}{dx^4} + 2 \dfrac{d^3 y}{dx^3} + 6 \dfrac{d^2 y}{dx^2} + 2 \dfrac{dy}{dx} + 5y = 0, \] then the general solution is ...........