Q. 285.0( 1 Vote )

Find the general solution of

Answer :


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we get P = -3 and Q = sin2x


This is linear differential equation where P and Q are functions of x


For the solution of linear differential equation, we first need to find the integrating factor


IF = e∫Pdx


IF = e∫(-3)dx


IF = e-3x


The solution of linear differential equation is given by y(IF) = ∫Q(IF)dx + c


Substituting values for Q and IF


ye-3x = ∫e-3xsin2x dx …. (1)


Let I = ∫e-3xsin2x dx


If u(x) and v(x) are two functions then by integration by parts,



Here v = sin 2x and u = e-3x


Applying the above formula, we get,




Again, applying the above stated rule in we get



So,








Put this value in (1) to get,


ye-3x = ∫e-3xsin2x dx




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