Solve the following differential equations:
Given
This is a first order linear differential equation of the form
Here, and Q = cos x
The integrating factor (I.F) of this differential equation is,
We have
[∵ m log a = log am]
∴ I.F = x2 [∵ elog x = x]
Hence, the solution of the differential equation is,
Recall
⇒ yx2 = x2sin x – 2{–x cos x + sin x} + c
⇒ yx2 = x2sin x + 2x cos x – 2 sin x + c
Thus, the solution of the given differential equation is