Q. 285.0( 1 Vote )

# Find the general solution of  Compare with we get P = -3 and Q = sin2x

This is linear differential equation where P and Q are functions of x

For the solution of linear differential equation, we first need to find the integrating factor

IF = e∫Pdx

IF = e∫(-3)dx

IF = e-3x

The solution of linear differential equation is given by y(IF) = ∫Q(IF)dx + c

Substituting values for Q and IF

ye-3x = ∫e-3xsin2x dx …. (1)

Let I = ∫e-3xsin2x dx

If u(x) and v(x) are two functions then by integration by parts, Here v = sin 2x and u = e-3x

Applying the above formula, we get,  Again, applying the above stated rule in we get So,      Put this value in (1) to get,

ye-3x = ∫e-3xsin2x dx  Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  Interactive Quiz on DIfferential Calculus50 mins  Interactive Quiz on Differential Calculus | Check Yourself56 mins  Functional Equations - JEE with ease48 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 