Embibe Experts Solutions for Exercise 3: EXERCISE 10.3

Integrating factor of the differential equation $\frac{dy}{dx}+\left(\frac{x}{1-x^2}\right)y=\sin x$ is

The solution of the differential equation $x\frac{dy}{dx}=-\frac{y}{2}-\frac{\sin 2x}{2y}$ is given by

A spherical rain drop evaporates at a rate proportional to its surface area at any instant $t.$ The rate of change of the radius of the rain drop is

If $y\left(t\right)$ is a solution of $\left(1+t\right)\frac{dy}{dt}-ty=1$ and $y\left(0\right)=1,$ then $y\left(1\right)$ is equal to

One of the solution of the differential equation, ${\left(\frac{dy}{dx}\right)}^2-x\frac{dy}{dx}+y=0$ may be

The differential equation $(x+y)dx+xdy=0,$ is

The differential equation $\frac{d^{2}y}{d{x}^2}+x\frac{dy}{dx}+\sin y+x^2=0$ is of the following type

If $y=y\left(x\right)$ satisfies $\frac{2+\sin x}{1+y}\left(\frac{dy}{dx}\right)=-\cos x,$ such that $y\left(0\right)=1,$ then $y\left(\frac{\pi }{2}\right)$ is equal to