Embibe Experts Solutions for Chapter: Differential Equation, Exercise 1: GUJCET 2017

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

The solution of the differential equation $2x\frac{dy}{dx}-y=0; y\left(1\right)=2$ represents .........

Particular solution of differential equation $e^{\frac{dy}{dx}}=x; y\left(1\right)=3;x>0$ is ........

The integrating factor of the differential equation $\frac{dy}{dx}=\frac{1}{x+y+2}$ is

The population of a city increases at the rate $3\%$ per year. If at time $t$ the population of city is $p,$ then find equation of $p$ in time $t.$