First slide

Methods of solving first order first degree differential equations

Question

The solution of the differential equation $(x^{4} + y^{4}) d x - x y^{3} d y = 0$ is

Moderate

A

$c x = e^{{(y / x)}^{4}}$
B

$c y = e^{{(y / x)}^{4}}$
C

$c y = e^{{(x / y)}^{3}}$
D

$c x = e^{x^{3} y}$

Solution

The given equation can be written as
$\begin{array}{l} \Rightarrow \frac{d y}{d x} = \frac{x^{4} + y^{4}}{x y^{3}} = {(\frac{x}{y})}^{3} + \frac{y}{x} \\ put y = v x then \frac{d y}{d x} =v+x \frac{d v}{d x} \\ \Rightarrow v + x \frac{d v}{d x} = \frac{1}{v^{3}} + v \\ \Rightarrow \int v^{3} d v = \int \frac{d x}{x} \\ \Rightarrow \frac{v^{4}}{4} = \log x + \log c = \log c x \\ \Rightarrow c x = e^{\frac{1}{v^{4}}} = e {(^{\frac{y}{x}})}^{4} \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App