Question

Which of the following differential equations has the same order and degree

• A. $\frac { d ^ { 4 } y } { d x ^ { 4 } } + 8 \left( \frac { d y } { d x } \right) ^ { 6 } + 5 y = e ^ { x }$
• B. $5 \left( \frac { d ^ { 3 } y } { d x ^ { 3 } } \right) ^ { 4 } + 8 \left( 1 + \frac { d y } { d x } \right) ^ { 2 } + 5 y = x ^ { 8 }$
• C. $\left[ 1 + \left( \frac { d y } { d x } \right) ^ { 3 } \right] ^ { 2 / 3 } = 4 \frac { d ^ { 3 } y } { d x ^ { 3 } }$
• D. $y = x ^ { 2 } \frac { d y } { d x } + \sqrt { 1 + \left( \frac { d y } { d x } \right) ^ { 2 } }$

Answer 1

Answer: (C)

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

Answer 2

Option (1) has order = 4, degree $= 1$

Option (2) has order = 3, degree $= 4$

Option (3) has order = 3, degree (taking cube)

Option (4) has order =1, degree $= 2$ (squaring).