Q. 265.0( 2 Votes )

Solve the following differential equations:

dx + xdy = e–ysec2ydy

Answer :

Given dx + xdy = e–ysec2ydy




This is a first order linear differential equation of the form



Here, P = 1 and e–ysec2y


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





We have


I.F = ey [ elog x = x]


Hence, the solution of the differential equation is,





Recall


xey = tan y + c



x = (tan y + c)e–y


Thus, the solution of the given differential equation is x = (tan y + c)e–y


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