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

If the Laplace transform of \(f(t)\) and \(f'(t)\) exist and \(F(s)\) is the Laplace transform of \(f(t)\), then \[ \lim_{s\to\infty}sF(s) \] is

Assertion (A): If \(X\sim N(\mu,\sigma^{2})\), then \[ P(X<\mu)=0.5. \] Reason (R): Normal distribution is symmetric about its mean.

The solution of \[ \frac{dy}{dx}+y=f(x), \] where \[ f(x)= \begin{cases} x, & 0\le x\\ 0, & x\ge1, \end{cases} \] with the conditions \[ y(0)=0,\qquad y(1)=e^{-1}, \] is

Which of the following series is divergent?

If \[ \vec{F}=(x+2y+az)\hat{i}+(bx-3y-z)\hat{j}+(4x+cy+2z)\hat{k} \] is irrotational, then $(a,b,c)$ is:

If $e^{\sin x}$ is an integrating factor of \[ \frac{dy}{dx}+(y-1)\cos x=e^{-\sin x}\cos x, \] then the general solution is:

Find $L\{t\,u(t-2)\}$.

The solution of \[ \frac{dy}{dx}+y=f(x), \] where \[ f(x)= \begin{cases} x, & 0\le x \\ 0, & x\ge1, \end{cases} \] with the conditions \[ y(0)=0,\qquad y(1)=e^{-1}, \] is

The maximum value of \(x^2 y z^3\), subject to \(x + y + z = 42\) exist at \((x, y, z) = (\alpha, \beta, \gamma)\), then \(\alpha\beta\gamma =\)

Given below are pair of functions \(f(x)\) and \(g(x)\). Which pair is not linearly independent?

The solution of \(\frac{\partial^2 u}{\partial t^2} = 4\frac{\partial^2 u}{\partial x^2}\), \(t > 0\), \(-\infty < x < \infty\) satisfying the conditions \(u(x,0) = x\) and \(\frac{\partial u}{\partial t}(x,0) = 0\) is