First slide

Methods of solving first order first degree differential equations

Question

$The solution of the DE 2 x^{3} y d y + (1 - y^{2}) (x^{2} y^{2} + y^{2} - 1) d x = 0 is$

Moderate

A

$x^{2} y^{2} = (c x - 1) (1 - y^{2})$
B

$x^{2} y^{2} = (c x + 1) (1 + y^{2})$
C

$x y = (c x + 1)$
D

$x y = 1 + y^{2}$

Solution

$\begin{array}{l} At Div by {(1 - y^{2})}^{2} \\ \frac{2 y}{{(1 - y^{2})}^{2}} \frac{d y}{d x} + \frac{y^{2}}{1 - y^{2}} \frac{1}{x} = \frac{1}{x^{3}} \\ Put \frac{y^{2}}{1 - y^{2}} = u \Rightarrow \frac{2 y}{{(1 - y^{2})}^{2}} \frac{d y}{d x} = \frac{d u}{d x} \\ \Rightarrow \frac{d u}{d x} + \frac{u}{x} = \frac{1}{x^{3}} I . F . = \int_{e}^{1} \frac{1}{x} a x = x \\ Solu. is x^{2} y^{2} = (c x - 1) (1 - y^{2}) \end{array}$

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