Embibe Experts Solutions for Chapter: Differential Equations, Exercise 1: MHT-CET 2019

Degree of the differential equation $e^{\frac{dy}{dx}}+{\left(\frac{dy}{dx}\right)}^3=x$  is

The general solution of the differential equation ${\sec }^{2}x$$\tan y$$dx+{\sec }^{2}y$$\tan x$$dy=0$ is

The integrating factor of the differential equation $\frac{dy}{dx}+\frac{1}{x}y=x^3-3$ is

The solution of the differential equation $x^2\frac{dy}{dx}=y^2+xy$ is

The particular solution of the differential equation ${\sin }^{2}y\frac{dx}{dy}+x=\cot y$, when $x=0$ and $y=\frac{3\pi }{4}$, is

In a certain culture of bacteria, the rate of increase is proportional to the number present. It is found that the number doubles in $4$ hours. Then, the number of times the bacteria are increased in $12$ hours is

The rate of growth of bacteria is proportional to the number present. If initially there were $1000$ bacteria and the number doubles in $1$ hour. Then, the number of bacteria after $2\frac{1 }{2}$ hours are $($Given $\left.\sqrt{2}=1.414\right)$

If the body cools from $135°\mathrm{C}$ to $80°\mathrm{C}$ at room temperature of $25°\mathrm{C}$ in $60$ minutes, then the temperature of body after $2$ hours is