Solve xy'(x) + (x+ 1)y(x) = 3xe¯ O a. y(x) = 3xe 2 + Ce O b. y(x) = - 3 + ce 2 Oc. O C. y(x) = (бх+3)e * ce %3D - 4x O d. y(x) = 3xln(x)e + cxe* %3D

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Q: Solve the differential equation by variation of parameters. 4x e2x y(x) = = y" - 4y =

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Q: 4. Solve (D-1)y (x'+2x +x+6)e using differential operators method.

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A: Explanation of the answer is as follows

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A: A detailed solution is given below.

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A: Please refer the attached image for complete solution.

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A: The solution is given as

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A: Given: D2-1y=x3+2x2+x+6e2x

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A: This question is based on solution of Homogeneous differential equation.

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A: Let y' = t Then , y''=dtdy  to find the value of y, integrate y' =t⇒∫dy =∫t. dt⇒      y =t22  So the…

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