Question

Find the degree of $[1+{\left(\frac{d^{2}y}{d{x}^2}\right)}^2]={[2+{\left(\frac{dy}{dx}\right)}^2]}^{3/2}$

• A. $4$
• B. $2$
• C. $1$
• D. $3$

Answer 1

The correct option is A $4$

Suppose that :$\frac{dy}{dx}=y_1$, $\frac{d^{2}y}{d{x}^2}=y_2$

Then, squaring both the sides of the given equation:

$[1+y_2^2{]}^2=[2+y_1^2{]}^3$

$\Rightarrow y_2^4+2y_2^2+1=[2+y_1^2{]}^3$
$\Rightarrow$ Order = $2$
degree = $4$.