# Solve the followi

Given

This is a first order linear differential equation of the form

Here, P = cos x and Q = sin x cos x

The integrating factor (I.F) of this differential equation is,

We have

I.F = esin x

Hence, the solution of the differential equation is,

Let sin x = t

cosxdx = dt [Differentiating both sides]

By substituting this in the above integral, we get

Recall

yet = tet – et + c

yet × e–t = (tet – et + c)e–t

y = t – 1 + ce–t

y = sin x – 1 + ce–sin x [ t = sin x]

Thus, the solution of the given differential equation is y = sin x – 1 + ce–sin x

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
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
RELATED QUESTIONS :

Integrating factoMathematics - Exemplar

Solve the followiRD Sharma - Volume 2

Solve the followiMathematics - Board Papers

Solve the followiRD Sharma - Volume 2

Solve the followiRD Sharma - Volume 2

Solve the followiRD Sharma - Volume 2

Solve the followiRD Sharma - Volume 2

Solve the followiRD Sharma - Volume 2

Solve the followiMathematics - Board Papers

Solve the followiRD Sharma - Volume 2