Q. 37 H5.0( 1 Vote )

Solve each of the

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


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