Q. 275.0( 1 Vote )

Solve the following differential equations:


Answer :

Given




This is a first order linear differential equation of the form



Here, P = –tan x and Q = –2 sin x


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





We have



[ m log a = log am]


[ elog x = x]


I.F = cos x


Hence, the solution of the differential equation is,





Let cos x = t


–sinxdx = dt [Differentiating both sides]


By substituting this in the above integral, we get



Recall




yt = t2 + c




[ t = cos x]


y = cos x + c sec x


Thus, the solution of the given differential equation is y = cos x + c sec x


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