Question

Solution of $y(2xy + e^{x})dx = e^{x}dy$ is

• A. $yx^{2} + e^{x} = cy$
• B. $xy^{2} + e^{x} = cx$
• C. $xy^{2} + e^{- x} = c$
• D. None of these

Answer 1

Answer: (A)

$yx^{2} + e^{x} = cy$

Answer 2

Re-writing the given equation,

$2xy^{2}dx + ye^{x}dx = e^{x}dy \Rightarrow 2xdx + \frac{ye^{x}dx - e^{x}dy}{y^{2}} = 0$

⇒ $d(x^{2}) + d\left( \frac{e^{x}}{y} \right) = 0$

Integrating, $x^{2} + \frac{e^{x}}{y} = c$

∴ $yx^{2} + e^{x} = cy$