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

The particular integral of $\left(D^4 - D^3 - 9D^2 - 11D - 4\right)y = e^{-x}$, where $D = \frac{d}{dx}$, is:}

Evaluate \[ \int_{-1}^{1}\frac{x^{2}\sin x}{x^{4}+1}\,dx. \]

The maximum value of \(x^{4}y^{3}\) such that \(x+y=42\) exists at \(x=\alpha,\; y=\beta\). Then \(\dfrac{\alpha}{\beta}\) in its lowest form is

If the solution of \[ \frac{d^2y}{dt^2} = -\frac54y+\frac{dy}{dt}, \] satisfying \[ y(0)=1, \qquad \left(\frac{dy}{dt}\right)_{t=0}=0, \] is \(y(t)\), then \(y(\pi)=\)