First slide

Types of solutions of differential equations

Question

$The acute angle between the two line passing through the origin and satisfying the differential$
$equation (4 x - 3 y) d x + (2 y - 3 x) d y = 0$

Moderate

A

$θ = \tan^{- 1} \frac{1}{3}$
B

$θ = \tan^{- 1} \frac{2}{3}$
C

$θ = \frac{π}{2}$
D

$θ = 0^{0}$

Solution

$4 x d x + 2 y d y - 3 (y d x + x d y) = 0$
$\begin{array}{l} 4 x d x + 2 y d y - 3 d (x y) = 0 \\ 2 x^{2} + y^{2} - 3 x y = c \\ (0, 0) \Rightarrow c = 0 hence (x - y) (2 x - y) = 0 \\ θ = \tan^{- 1} \frac{1}{3} (\sin c e \tan θ = |\frac{m_{1} - m_{2}}{1 + m_{1} m_{2}}|) \end{array}$

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