First slide

Methods of solving first order first degree differential equations

Question

$The solution of differential equation 2 y \sin x (\frac{d y}{d x}) = 2 \sin x \cos x - y^{2} \cos x at x = \frac{π}{2}, y = 1 is$

Moderate

A

$y^{2} = \sin x$
B

$y = \sin^{2} x$
C

$y^{2} = \cos x + 1$
D

None

Solution

$\begin{array}{l} Given equation can be rewrite as \\ 2 y \frac{d y}{d x} + y^{2} \cot x = \frac{d v}{d x} \\ Put y^{2} = v = 2 y \frac{d y}{d x} = \frac{d v}{d x} \\ \frac{d v}{d x} + v \cot x = 2 \cos x \\ If e^{\int \frac{\cos x}{\sin x} = d x = e^{\log \sin x}} = \sin x \\ Solution is v \sin x + \int 2 \cos x \sin x d x + c \\ y^{2} \sin x = \sin^{2} x + c; when x = \frac{π}{2}, y = 1 \\ 1 = 1 + c \Rightarrow c = 0; y^{2} \sin x = \sin^{2} x \Rightarrow y^{2} = \sin x \end{array}$

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