Embibe Experts Solutions for Chapter: Differential Equation, Exercise 1: KEAM 2020

The order and degree of the differential equation $\frac{{\mathrm{d}}^2\mathrm{y}}{{\mathrm{dx}}^2}+\sqrt{{\mathrm{x}}^2+{\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)}^{3/2}}=0$ are respectively

Elimination of arbitrary constants $\mathrm{A}$ and $\mathrm{B}$ from $\mathrm{y}=\frac{\mathrm{A}}{\mathrm{x}}+\mathrm{B}, \mathrm{x}>0$ leads to the differential equation

The differential equation of all circles passing through origin and having their centres on the $X$-axis is

The differential equation of the family of curves $y=e^x\left(A\cos x+B\sin x\right)$$,$ where $A$ and $B$ are arbitrary constants is

The equation of the curve that passes through the point $(1, 2)$ and satisfies $\frac{dy}{dx}=\frac{-2xy}{x^2+1}$ is

The general solution of $\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{2\mathrm{x}-\mathrm{y}}{\mathrm{x}+2\mathrm{y}}$ is given by

The general solution of the differential equation ${\mathrm{xy}}^{\text{'}}+\mathrm{y}={\mathrm{x}}^2,\mathrm{x}>0$ is

The integrating factor of the differential equation $3{\mathrm{xy}}^{\text{'}}-\mathrm{y}=1+\mathrm{logx},\mathrm{x}>0$ is