PYQs Based Test - 17 : Engineering Mathematics

The particular solution of the initial value problem given below is:

$\frac{d^{2}y}{d{x}^2}+12\frac{dy}{dx}+36y=0$, with y(0) = 3 and $\frac{dy}{dx}{|}_{x=0}=-36$

The contour C given below is on the complex plane z = x + jy, where $\mathrm{j}=\sqrt{-1}$



The value of the integral $\frac{1}{\pi \mathrm{j}}\underset{\mathrm{c}}{\oint }\frac{\mathrm{dz}}{{\mathrm{z}}^2-1}$ is _______

The minimum value of the function $f\left(x\right)=\frac{1}{3}x\left(x^2-3\right)$ in the interval - 100 ≤ x ≤ 100 occurs at x = __________.

Consider the integral ${\oint }_C\frac{\sin (x)}{x^2(x^2+4)}dx$

Where C is a counter-clockwise oriented circle defined as |x - i| = 2. The value of the integral is

Consider the homogeneous ordinary differential equation $x^2\frac{d^{2}y}{d{x}^2}-3x\frac{dy}{dx}+3y=0,$ x > 0 with y(x) as a general solution. Given that y(1) = 1 and y(2) = 14 the value of y(1.5), rounded off to two decimal places, is ______.