G Tewani Solutions for Chapter: Differential Equations, Exercise 1: DPP

The solution of the differential equation $\left(x^2-x^{2}y\right)\frac{\mathit{d}y}{\mathit{d}x}+y^2+x{y}^2=0$ is:

The family of curves passing through $(0,0)$ and satisfying the differential equation $\frac{y_2}{y_1}=1$ (where $y_n=\frac{d^{n}y}{d{x}^n}$), is

The solution of the differential equation $y^{2}dx+\left(x^2-xy+y^2\right)dy=0$ is:

The solution of differential equation $\left(1-xy+x^2{y}^2\right)dx=x^{2}dy$ is

The differential equation for the family of curves $y=c \sin x$ can be given by

If the solution of the equation $\frac{d^{2}x}{d{t}^2}+4\frac{dx}{dt}+3x=0$ given that for $t=0, x=0$ and $\frac{dx}{dt}=12$ is in the form $x=A{e}^{-3t}+B{e}^{-t}$, then

The solution of ${\left(\frac{dy}{dx}\right)}^2-2\left(x+\frac{1}{4x}\right)\frac{dy}{dx}+1=0$

${\left(\frac{dy}{dx}\right)}^2+2y\cot x\frac{dy}{dx}=y^2$ has the solution