First slide

Methods of solving first order first degree differential equations

Question

$Solution of the differential equation (x + 2 y^{3}) \frac{d y}{d x} = y is$

Moderate

A

$x = y (c + y^{2})$
B

$x = y (c - y^{2})$
C

$y = x (c + y^{2})$
D

$y = x (c - x^{2})$

Solution

$\begin{array}{l} x + 2 y^{3} = y \cdot \frac{d x}{d y} \Rightarrow \frac{d x}{d y} - \frac{1}{y} x = 2 y^{2} \\ I.F. = e^{\int p \cdot d y} = \frac{1}{y} solution is x \cdot \frac{1}{y} = \sqrt{2} y^{2} \cdot \frac{1}{y} d y = y^{2} + c \end{array}$

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