#### please solve RD sharma class 12 chapter 21 Differential Equation exercise 21.1 question 7 maths textbook solution

Order=4 , Degree=2 , Non-linear

Hint:

The order is the highest numbered derivative in the equation with no negative or fractional power of the dependent variable and its derivatives, while the degree is the highest power to which a derivative is raised.

Given:

$\frac{d^{4}y}{dx^{4}}=\left [ c+\left ( \frac{dy}{dx} \right )^{2} \right ]^{\frac{3}{2}}$

Solution:

Since this equation has fractional powers, we need to remove them.

So squaring on both sides, we get

$\left (\frac{d^{4}y}{dx^{4}} \right )^{2}=\left [ c+\left ( \frac{dy}{dx} \right )^{2} \right ]^{3}$
Solving both sides,

$\left (\frac{d^{4}y}{dx^{4}} \right )^{2}=c^{3}+\left ( \frac{dy}{dx} \right )^{6}+3c^{2}\left ( \frac{dy}{dx} \right )^{2}+3c\left ( \frac{dy}{dx} \right )^{4}$

So, in this question, the order of the differential equation is 4 and the degree of the differential equation is 2.

In a differential equation, when the dependent variable and their derivatives are only multiplied by constant or independent variable, then the equation is linear.

So, in this question. The dependent variable is y and the term $\frac{dy}{dx}$ is multiplied by itself, also the degree of the

equation is 2 which must be one for the equation to be linear. So the given equation is non-linear.

Therefore, Order=4 , Degree=2 , Non-linear