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Solve the following IVPs using Laplace Transform: 1) dy dt 3y(t) = e4t; y(0) = 0

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Giwen differential equation: dy 341H = e dt y-34 = ett Appleging Laplace transform Onboth sides. Lhy }= Lheutz L{y }- 31{y}= Lhetty 34 AS Lhy}= Y(s) L{yy= SY(s)- yo) Lhetty = 1 5-4و + ما = 3Ly3 - 13 ... ) = (يلا 3- ام9 - (sالای و - ا = (0) - (لالی) (= - Giwen initial Condition y(0) =0 و ۵۰ - (لا (د) YIslApplying inverse both sides. laplace trans foon on بما {\{YS) Y = [{{4- & } =) y(t) = [{{4}-thab As Ilsa 3 eat = y(t = et

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Solve the following IVPs using Laplace Transform: 1) dy dt 3y(t) = e4t; y(0) = 0
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