Q. 37 M5.0( 1 Vote )

Solve each of the following initial value problems:

,

Answer :

,


Given and



This is a first order linear differential equation of the form



Here, P = cot x and Q = 2 cos x


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




We have



I.F = sin x [ elog x = 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




yt = t2 + c




[ t = sin x]


However, when, we have y = 0




0 = 1 + c


c = –1


By substituting the value of c in the equation for y, we get






[ sin2θ + cos2θ = 1]


y = –cos x cot x


Thus, the solution of the given initial value problem is y = –cosec x cot x


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 CalculusFREE Class
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