(D^2-5D-6)y=18x^2+12e^2x

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Solution for (D^2-5D-6)y=18x^2+12e^2x equation: 


Simplifying
(D2 + -5D + -6) * y = 18x2 + 12e2x

Reorder the terms:
(-6 + -5D + D2) * y = 18x2 + 12e2x

Reorder the terms for easier multiplication:
y(-6 + -5D + D2) = 18x2 + 12e2x
(-6 * y + -5D * y + D2 * y) = 18x2 + 12e2x
(-6y + -5yD + yD2) = 18x2 + 12e2x

Reorder the terms:
-6y + -5yD + yD2 = 12e2x + 18x2

Solving
-6y + -5yD + yD2 = 12e2x + 18x2

Solving for variable 'y'.

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

Reorder the terms:
-12e2x + -18x2 + -6y + -5yD + yD2 = 12e2x + 18x2 + -12e2x + -18x2

Reorder the terms:
-12e2x + -18x2 + -6y + -5yD + yD2 = 12e2x + -12e2x + 18x2 + -18x2

Combine like terms: 12e2x + -12e2x = 0
-12e2x + -18x2 + -6y + -5yD + yD2 = 0 + 18x2 + -18x2
-12e2x + -18x2 + -6y + -5yD + yD2 = 18x2 + -18x2

Combine like terms: 18x2 + -18x2 = 0
-12e2x + -18x2 + -6y + -5yD + yD2 = 0

The solution to this equation could not be determined.

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