Question

Find the general solution of the differential equation. $x y\,{\frac{d y}{d x}}=(x+2)(y+2).$

A die is rolled. If E = {1, 3, 5}, F = {2, 3} and G = {2, 3, 4, 5}, find (a) P(E U F)/G] (b)P [(E ∩ F)/G].

If x changes from 4 to 4·01, then find the approximate change in log x.

If A = $\begin{vmatrix}2 & 3 & -1 \\ 4 & 1 & 0 \\ 3 & 3 & 2\end{vmatrix}$ , find $M_{12}\times M_{21}+C_{21}\times C_{12}$ when $M_{i j}$ is called minor and $C_{i j}$ is called co-factors of A.

The volume of a cube is increasing at the rate of 9 cm³/sec. How fast is the surface area increasing when the length of an edge is 10 cm.

For the curve y = 5x – 2x³, if x increases at the rate of 2 units/sec, then find the rate of change of the slope of the curve when x = 3.

From the differential equation of equation y = a cos 2x + b sin 2x, where a and b are constant.