Answer :

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


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