First slide

Types of solutions of differential equations

Question

$The solution of differential equation y d x - (1 + e^{- x} y^{2}) d y = 0 is$

Moderate

A

$\frac{e^{y}}{x} = y + c$
B

$e^{x} = y^{2} + c y$
C

$e^{y} = y^{2} + c x$
D

$e^{x} = y^{2} + c x$

Solution

$\begin{array}{l} y d x - d y = e^{- x} y^{2} d y \\ \frac{e^{x} (y d x - d y)}{y^{2}} = d y \\ \Rightarrow d (\frac{e^{x}}{y}) = d y integrations both sides e^{x} = y^{2} + c y \end{array}$

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