Question

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

Form the differential equation representing family of curves given by (x – a)² + 2y²= a², where a is an arbitrary constant.

Find the equations of the normal to the curve x² = 4y which passes through the point (1, 2).

Find the particular solution of the differential equation : ${\frac{d y}{d x}}\ +y\cot x=2x+x^{2}\cot x,$ x ≠ 0. Given that y = 0, when $x={\frac{\pi}{2}}\ .$

Find the particular solution of differential equation : ${\frac{d y}{d x}}=-{\frac{x+y\cos x}{1+\sin x}}$ given that y = 1 when x = 0.

Find the equation of the normal at the point (am², am³) for the curve ay² = x³.

Solve the following differential equation. $(x^{3}+x^{2}+x+1){\frac{d y}{d x}}=2x^{2}+x.$