Maharashtra Board Solutions for Chapter: Differential Equations, Exercise 6: MISCELLANEOUS EXERCISE 6

The order and degree of the differential equation $\sqrt{1+{\left(\frac{dy}{dx}\right)}^2}={\left(\frac{d^{2}y}{d{x}^2}\right)}^{\frac{3}{2}}$ are respectively ...

The differential equation of $y=c^2+\frac{c}{x}$ is .......

$x^2+y^2=a^2$ is a solution of $. . .$

The differential equation of all circles having their centers on the line $y=5$ and touching the $X$-axis is

Find the order and degree of differential equation ${\left(\frac{d^{3}y}{d{x}^3}\right)}^2=\sqrt[5]{1+\frac{dy}{dx}}$. State also whether it is linear or non-linear.

Verify that $x^2=2y^2\log y$ is a solution of the differential equation $x^2+y^2=xy\frac{dx}{dy}$.

Solve the following differential equation :

$y\log y=\left(\log y^2-x\right)\frac{dy}{dx}$

Solve the differential equation $4\frac{dx}{dy}+8x=5e^{-3y}$