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Non-linear DE using laplace transform...

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Hi, I have an assignment and a subproblem of one of the problems is about solving a differential equation using the Laplace transform. The problem is it is nonlinear and so when applying the transform, I end up with both F(s) and the integral of F(s) in the same equation, so I cannot isolate F(s). I have already solved it using another technique (this was the objective of the previous subproblem). My question is: Is this possible at all? Could this be an oversight on their part?

You can see the form of the equation below. Only Y and t are variables.

dY/dt + (a/(b+a*t) + c)*Y = d / (b+a*t)

You can see that in the second term we have Y in the numerator and t in the denominator, making the equation nonlinear... I decomposed the fraction into partial fractions in order to get only t in the denominator and apply the Laplace transform property that L(f(t)/t) = integral from s to infinity F(s)ds, but so I get another integral-differential equation...

Thanks in advance.

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