Question

The degree of the differential equation

$y ( x ) = 1 + \frac { d y } { d x } + \frac { 1 } { 1.2 } \left( \frac { d y } { d x } \right) ^ { 2 } + \frac { 1 } { 1.2 .3 } \left( \frac { d y } { d x } \right) ^ { 3 } + \ldots$ is

• A. 2
• B. 3
• C. 1
• D. None of these

Answer 1

Answer: (C)

1

Answer 2

$y = 1 + t + \frac { t ^ { 2 } } { 2 ! } + \frac { t ^ { 3 } } { 3 ! } + \ldots + \infty$ where $t = \frac { d y } { d x }$

⇒ $y = e ^ { t }$ , ∴ $t = \log y$ ⇒ $\frac { d y } { d x } = \log y$.

Hence degree is 1.