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

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


Simplifying
(D4 + 2D3 + -2d2) * y = x2 + 3e2x + 4sinx

Reorder the terms:
(2D3 + D4 + -2d2) * y = x2 + 3e2x + 4sinx

Reorder the terms for easier multiplication:
y(2D3 + D4 + -2d2) = x2 + 3e2x + 4sinx
(2D3 * y + D4 * y + -2d2 * y) = x2 + 3e2x + 4sinx

Reorder the terms:
(-2d2y + 2yD3 + yD4) = x2 + 3e2x + 4sinx
(-2d2y + 2yD3 + yD4) = x2 + 3e2x + 4sinx

Reorder the terms:
-2d2y + 2yD3 + yD4 = 3e2x + 4insx + x2

Solving
-2d2y + 2yD3 + yD4 = 3e2x + 4insx + x2

Solving for variable 'd'.

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

Add '-2yD3' to each side of the equation.
-2d2y + 2yD3 + -2yD3 + yD4 = 3e2x + 4insx + x2 + -2yD3

Combine like terms: 2yD3 + -2yD3 = 0
-2d2y + 0 + yD4 = 3e2x + 4insx + x2 + -2yD3
-2d2y + yD4 = 3e2x + 4insx + x2 + -2yD3

Add '-1yD4' to each side of the equation.
-2d2y + yD4 + -1yD4 = 3e2x + 4insx + x2 + -2yD3 + -1yD4

Combine like terms: yD4 + -1yD4 = 0
-2d2y + 0 = 3e2x + 4insx + x2 + -2yD3 + -1yD4
-2d2y = 3e2x + 4insx + x2 + -2yD3 + -1yD4

Divide each side by '-2y'.
d2 = -1.5e2xy-1 + -2insxy-1 + -0.5x2y-1 + D3 + 0.5D4

Simplifying
d2 = -1.5e2xy-1 + -2insxy-1 + -0.5x2y-1 + D3 + 0.5D4

Reorder the terms:
d2 = D3 + 0.5D4 + -1.5e2xy-1 + -2insxy-1 + -0.5x2y-1

Reorder the terms:
-1D3 + -0.5D4 + d2 + 1.5e2xy-1 + 2insxy-1 + 0.5x2y-1 = D3 + 0.5D4 + -1.5e2xy-1 + -2insxy-1 + -0.5x2y-1 + -1D3 + -0.5D4 + 1.5e2xy-1 + 2insxy-1 + 0.5x2y-1

Reorder the terms:
-1D3 + -0.5D4 + d2 + 1.5e2xy-1 + 2insxy-1 + 0.5x2y-1 = D3 + -1D3 + 0.5D4 + -0.5D4 + -1.5e2xy-1 + 1.5e2xy-1 + -2insxy-1 + 2insxy-1 + -0.5x2y-1 + 0.5x2y-1

Combine like terms: D3 + -1D3 = 0
-1D3 + -0.5D4 + d2 + 1.5e2xy-1 + 2insxy-1 + 0.5x2y-1 = 0 + 0.5D4 + -0.5D4 + -1.5e2xy-1 + 1.5e2xy-1 + -2insxy-1 + 2insxy-1 + -0.5x2y-1 + 0.5x2y-1
-1D3 + -0.5D4 + d2 + 1.5e2xy-1 + 2insxy-1 + 0.5x2y-1 = 0.5D4 + -0.5D4 + -1.5e2xy-1 + 1.5e2xy-1 + -2insxy-1 + 2insxy-1 + -0.5x2y-1 + 0.5x2y-1

Combine like terms: 0.5D4 + -0.5D4 = 0.0
-1D3 + -0.5D4 + d2 + 1.5e2xy-1 + 2insxy-1 + 0.5x2y-1 = 0.0 + -1.5e2xy-1 + 1.5e2xy-1 + -2insxy-1 + 2insxy-1 + -0.5x2y-1 + 0.5x2y-1
-1D3 + -0.5D4 + d2 + 1.5e2xy-1 + 2insxy-1 + 0.5x2y-1 = -1.5e2xy-1 + 1.5e2xy-1 + -2insxy-1 + 2insxy-1 + -0.5x2y-1 + 0.5x2y-1

Combine like terms: -1.5e2xy-1 + 1.5e2xy-1 = 0.0
-1D3 + -0.5D4 + d2 + 1.5e2xy-1 + 2insxy-1 + 0.5x2y-1 = 0.0 + -2insxy-1 + 2insxy-1 + -0.5x2y-1 + 0.5x2y-1
-1D3 + -0.5D4 + d2 + 1.5e2xy-1 + 2insxy-1 + 0.5x2y-1 = -2insxy-1 + 2insxy-1 + -0.5x2y-1 + 0.5x2y-1

Combine like terms: -2insxy-1 + 2insxy-1 = 0
-1D3 + -0.5D4 + d2 + 1.5e2xy-1 + 2insxy-1 + 0.5x2y-1 = 0 + -0.5x2y-1 + 0.5x2y-1
-1D3 + -0.5D4 + d2 + 1.5e2xy-1 + 2insxy-1 + 0.5x2y-1 = -0.5x2y-1 + 0.5x2y-1

Combine like terms: -0.5x2y-1 + 0.5x2y-1 = 0.0
-1D3 + -0.5D4 + d2 + 1.5e2xy-1 + 2insxy-1 + 0.5x2y-1 = 0.0

The solution to this equation could not be determined.

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