The solution of the differential equation d y/d x - 2 y 2 x = e^{x} 2 x is

Correct Answer is : ycos⁡2x=ex+Cy 2 x = e^{x} + Cycos2x=ex+C

Correct Answer is : ycos⁡2x=ex+Cy 2 x = e^{x} + Cycos2x=ex+C

Test Index

AP EAMCET Engineering 2013 Solved Paper

Section: Mathematics

Question : 160 of 160

Marks: +1, -0

\frac{d y}{d x} - 2 y \tan 2 x = e^{x} \sec 2 x

Solution:

Given, differential equation is

\frac{d y}{d x} - 2 y \tan 2 x = e^{x} \sec 2 x

Here,

P = 2 \tan 2 x, Q = e^{x} \sec 2 x

∴

IF = e^{\int -2 \tan 2 x \, d x}

= e^{\frac{-2 \log \sec 2 x}{2}}

= e^{-\log \sec 2 x}

= \frac{1}{\sec 2 x}

∴ Required solution is

\frac{y}{\sec 2 x} = \int e^{x} \cdot \frac{1}{\sec 2 x} \cdot \sec 2 x \, d x + C

⇒

y \cos 2 x = \int e^{x} \cdot 1 \, d x + C

⇒

y \cos 2 x = e^{x} + C

where, C is the constant of integration.

Go to Question:

Prev Question