Question

Find : $\large\textstyle\int$$\large{\frac{x}{(x^{2}+1)(x-1)}}\,d x.$

The equation of tangent at (2, 3) on the curve y² = ax³ + b is y = 4x – 5. Find the values of a and b.

Probability of solving specific problem independently by A and B are 1/2 and 1/3 respectively. If both try to solve the problem, independently, then find the probability that (i) the problem is solved (ii) exactly one of them solves the problem

Find the particular solution of the differential equation : $y e^{y}\,d x=(y^{3}+2x e^{y})d y,y(0)=1$

Find the particular solution of the following differential equation : ${\frac{d y}{d x}}\;=1+x^{2}+y^{2}+x^{2}y^{2},$ given that y = 1, when x = 0.

Find the particular solution of the following differential equation : ${\frac{d y}{d x}}-y=\cos x\ {\mathrm{~for~}}x=0,y=1.$

A and B throw a pair of dice alternately. A wins the game if he gets a total of 9 and B wins if he gets a total of 7. If A starts the game, find the probability of winning the game by B.