First slide

Methods of solving first order first degree differential equations

Question

$The solution of the D.E (x + 2 y^{3}) \frac{d y}{d x} = y is$

Moderate

A

$\frac{x}{y^{2}} =y+C$
B

$\frac{x}{y} {=y}^{2} +C$
C

$\frac{x^{2}}{y} {=y}^{2} +C$
D

$\frac{y}{x} {=x}^{2} +C$

Solution

$y \frac{d x}{d y} = x + 2 y^{3}$
$\frac{d x}{d y} - \frac{x}{y} = 2 y^{2}$
$\begin{array}{l} I . F = e^{- \int \frac{1}{y} dy} = e^{- \log y} = y^{- 1} = \frac{1}{y} \\ Solution of the D.E in \frac{x}{y} = \int 2 ydy = y^{2} + C \end{array}$

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