First slide

Introduction to Differential equations

Question

$If (x + 2 y^{3}) \frac{d y}{d x} = y then$

Moderate

A

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

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

$\frac{x}{y} - y^{2} = c$
D

$\frac{y}{x} - x^{2} = c$

Solution

$\begin{aligned} \frac{d x}{d y} = \frac{x}{y} + 2 y^{2} I.F. = \exp \int \frac{- 1}{y} d x = \frac{1}{y} \\ ∴ Solution is \frac{x}{y} = \int 2 y^{2} \frac{1}{y} d y = y^{2} + c \end{aligned}$

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