R D Sharma Solutions for Chapter: Differential Equations, Exercise 13: MULTIPLE CHOICE QUESTIONS (MCQs)

The differential equation of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=C$ is

Find the solution of the differential equation  $\frac{dy}{dx}+\frac{y}{x}=\sin x$.

The equation of the curve satisfying the differential equation $y\left(x+y^3\right)dx=x\left(y^3-x\right)dy$ and passing through the point $(1,1)$ is

Find solution of the differential equation  $2x\frac{dy}{dx}-y=3$.

Find the solution of the differential equation $x\frac{dy}{dx}=y+x \tan \frac{y}{x}$.

The differential equation satisfied by $a{x}^2+b{y}^2=1$ is

Which of the following transformations reduce the differential equation $\frac{dz}{dx}+\frac{z}{x}\log z=\frac{z}{x^2}(\log z{)}^2$ into the form $\frac{du}{dx}+P\left(x\right)u=Q\left(x\right)$

Find the solution of the differential equation  $\frac{dy}{dx}=\frac{y}{x}+\frac{\varphi \left(\frac{y}{x}\right)}{\varphi \text{'}\left(\frac{y}{x}\right)}$.