Question

The solution of the differential equation

$x \cos y d y = \left( x e ^ { x } \log x + e ^ { x } \right) d x$ is

• A. $\sin y = \frac { 1 } { x } e ^ { x } + c$
• B. $\sin y + e ^ { x } \log x + c = 0$
• C. $\sin y = e ^ { x } \log x + c$
• D. None of these

Answer 1

Answer: (C)

$\sin y = e ^ { x } \log x + c$

Answer 2

$x \cos y d y = \left( x e ^ { x } \log x + e ^ { x } \right) d x$

⇒ $\cos y d y = \left( e ^ { x } \log x + \frac { e ^ { x } } { x } \right) d x$

On integrating, $\sin y = e ^ { x } \log x + c$.