First slide

Methods of solving first order first degree differential equations

Question

$The solution of \frac{d y}{d x} = \frac{x - 2 y + 3}{2 x - y + 5} is$

Moderate

A

$x^{2} {-4xy+y}^{2} +6x-10y=c$
B

$x^{2} {-4xy+y}^{2} +6x+10y=c$
C

$x^{2} {+4xy+y}^{2} +6x-10y=c$
D

$x^{2} {-4xy-y}^{2} -6x-10y=c$

Solution

$\begin{array}{l} 2 xdy - ydy + 5 dy = xdx - 2 ydx + 3 dx \\ \to 2 (xdy + ydx) - ydy + 5 dy = xdx + 3 dx \\ \to \int 2 d (xy) - ydy + 5 dy = \int xdx + 3 dx \\ \to 2 xy - \frac{y^{2}}{2} + 5 y = \frac{x^{2}}{2} + 3 x \\ \to 4 xy - y^{2} + 10 y = x^{2} + 6 x + c \\ \to x^{2} - 4 xy + y^{2} + 6 x - 10 y = c \end{array}$

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