Question

The degree of the differential equation $ \frac{{{d}^{2}}y}{d{{x}^{2}}}=\frac{5y+\frac{dy}{dx}}{\sqrt{\frac{{{d}^{2}}y}{d{{x}^{2}}}}} $ is equal to

• A. $ 2 $
• B. $ 3 $
• C. $ 4 $
• D. $ 5/2 $

Answer 1

Answer: (B)

$ \frac{{{d}^{2}}y}{d{{x}^{2}}}=\frac{5y+\frac{dy}{dx}}{\sqrt{{{d}^{2}}y/d{{x}^{2}}}} $
$ {{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{3/2}}=5y+\frac{dy}{dx} $
Squaring on both sides, $ {{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{3}}={{\left( 5y+\frac{dy}{dx} \right)}^{2}} $
So, the degree of given differential equation is 3.