Q. 35.0( 2 Votes )

Solve the following differential equations :


Answer :

Formula:-


(i) if a differential equation is ,


then y(I.F) = ∫Q.(I.F)dx + c, where I.F = e∫Pdx


(ii) ∫dx = x + c



Here,


This is a linear differential equation, comparing it with



P = 2, Q = 6ex


I.F = e∫Pdx


= e∫2Pdx


= e2x


Solution of the equation is given by


y(I.F) = ∫Q.(I.F)dx + c


ye2x = ∫6ex e2x dx + c


ye2x = ∫6e3x dx + c



ye2x = 2e3x + c


y = 2e3x + ce–2x


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