Question

The degree of the differential equation

$\left( 1 + \left( \frac { d y } { d x } \right) ^ { 2 } \right) ^ { 3 / 4 } = \left( \frac { d ^ { 2 } y } { d x ^ { 2 } } \right) ^ { 1 / 3 }$ is

• A. $\frac { 1 } { 3 }$
• B. 4
• C. 9
• D. $\frac { 3 } { 4 }$

Answer 1

Answer: (B)

4

Answer 2

$\left[ 1 + \left( \frac { d y } { d x } \right) ^ { 2 } \right] ^ { 3 / 4 } = \left( \frac { d ^ { 2 } y } { d x ^ { 2 } } \right) ^ { 1 / 3 }$ ⇒ $\left[ 1 + \left( \frac { d y } { d x } \right) ^ { 2 } \right] ^ { 9 } = \left( \frac { d ^ { 2 } y } { d x ^ { 2 } } \right) ^ { 4 }$

Clearly, degree is 4.