The equation y" + 4y'+ 6y = 2et where y(0) = 5,y'(0) = 0 when solved using Laplace transform, produced %3D L(y) As²+Bs+C (s²+4s+D)(s+1) Match the following values.

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A: GIVEN: dydx=2xsin2y+(2 siny)/x22x2cosx-(2cosy)/x             (2x2y siny -x y3sinx)dx +(x3siny +x3 y…

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A: The solution is given as

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A: Note: The coefficient of the third and 4th power of (x-1) is incorrect in the given answer. We are…

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A: We can find the integral as below.

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Q: Please review the screenshot attached to this request and solve the problem :)

A: Step 1: Step 2: Step 3: Step 4: