#### Provide solution for RD sharma maths class 12 chapter 21 Differential Equation exercise 21.1 question 8

Order=1 , Degree=2 , 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:

$x+\frac{dy}{dx}=\sqrt{1+\left ( \frac{dy}{dx} \right )^{2}}$

Solution:

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

So squaring on both sides, we get

$\left (x+\frac{dy}{dx} \right )^{2}=1+\left ( \frac{dy}{dx} \right )^{2}\Rightarrow x^{2}+\left ( \frac{dy}{dx} \right )^{2}+2x\frac{dy}{dx}=1+\left ( \frac{dy}{dx} \right )^{2}$

$x^{2}+2x\frac{dy}{dx}-1=0$

So, in this question, the order of the differential equation is 1 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 its derivatives are multiplied with a constant or independent variable only. So this equation is linear differential equation.

Therefore, Order=1 , Degree=2 , linear

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