Q 1: The ratio
\frac{\int_{x_1}^{x_2}{\displaystyle\frac{dy}x}}{{\displaystyle\frac{x_2-x_1}y}\;at\;x=x_2}(x_2>x_1),Where is 1/y a monotonically increasing function of x, is
Q 2: Solve \frac{d^2y}{dx^2}-m^2y=0 subject to y = 1 at x = 0 and \frac{dy}{dx}=0 at x = 1.
Q 3: Given the matrix \overset=A=\begin{bmatrix}-1&-2\\3&4\end{bmatrix} (a) write down the characteristic equation, (b) compute \left(\overset=A\right)^4 without direct multiplication.
Q 4: Solve \frac{dy}{dx}+0.6y=6e^{-0.5x} using the integrating factor method, given y = 1 at x = 0.