First slide

Methods of solving first order first degree differential equations

Question

$If x \cdot \ln x \cdot \frac{d y}{d x} + y = 2 \ln x, y (e) = 2 then y (e^{2}) =$

Moderate

A

1
B

$\frac{3}{2}$
C

2
D

$\frac{5}{2}$

Solution

$\begin{array}{l} \frac{d y}{d x} + \frac{y}{x \cdot \ln x} = \frac{2}{x} \\ I.F = \exp \int \frac{d x}{x \cdot \ln x} = \ln x \\ ∴ soln is y \cdot \ln x = 2 \int \frac{\ln x}{x} d x \\ y \ln x = (\ln x)^{2} + c \\ y = (\ln x) + \frac{1}{\ln x} \\ y (e^{2}) = 2 + \frac{1}{2} = \frac{5}{2} \end{array}$

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