(D^4+2D^3-3D^2)y=x^2+3e^2x

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Solution for (D^4+2D^3-3D^2)y=x^2+3e^2x equation: 


Simplifying
(D4 + 2D3 + -3D2) * y = x2 + 3e2x

Reorder the terms:
(-3D2 + 2D3 + D4) * y = x2 + 3e2x

Reorder the terms for easier multiplication:
y(-3D2 + 2D3 + D4) = x2 + 3e2x
(-3D2 * y + 2D3 * y + D4 * y) = x2 + 3e2x
(-3yD2 + 2yD3 + yD4) = x2 + 3e2x

Reorder the terms:
-3yD2 + 2yD3 + yD4 = 3e2x + x2

Solving
-3yD2 + 2yD3 + yD4 = 3e2x + x2

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Reorder the terms:
-3e2x + -1x2 + -3yD2 + 2yD3 + yD4 = 3e2x + x2 + -3e2x + -1x2

Reorder the terms:
-3e2x + -1x2 + -3yD2 + 2yD3 + yD4 = 3e2x + -3e2x + x2 + -1x2

Combine like terms: 3e2x + -3e2x = 0
-3e2x + -1x2 + -3yD2 + 2yD3 + yD4 = 0 + x2 + -1x2
-3e2x + -1x2 + -3yD2 + 2yD3 + yD4 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-3e2x + -1x2 + -3yD2 + 2yD3 + yD4 = 0

The solution to this equation could not be determined.

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