Q. 395.0( 1 Vote )

Find the general solution of the differential equation

Answer :

Given



This is a first order linear differential equation of the form



Here, P = –1 and Q = cos x


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





We have


I.F = e–x


Hence, the solution of the differential equation is,






Let








I = e–x(sin x – cos x) – I


2I = e–x(sin x – cos x)



By substituting the value of I in the original integral, we get





Thus, the solution of the given differential equation is


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