First slide

Introduction to Differential equations

Question

$The solution of \frac{d y}{d x} + 2 y t a n x = \sin x, given that y = 0, x = π / 3 is$

Moderate

A

${y=cosx-2cos}^{2} x$
B

${y=cosx+2cos}^{2} x$
C

${y=cosx-cos}^{2} x$
D

${y=2cosx-2cos}^{2} x$

Solution

$\begin{array}{l} I . F = e^{\int 2 t tax d x} = e^{2 \log | \sec x |} = \sec^{2} x \\ Solution of the differential equation is {ysec}^{2} x == \int \frac{\sin x}{\cos^{2} x} dx \\ = \int \sec x \tan x d x = \sec x + c \\ If x = π / 3 \to 4 y = 2 + c \\ y = 0 \Rightarrow c = - 2 \\ \Rightarrow {ysec}^{2} x = secx - 2 \\ y = \cos x - 2 \cos^{2} x \end{array}$

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