(D^2-5D+6)y=12x*e^3x

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Solution for (D^2-5D+6)y=12x*e^3x equation: 


Simplifying
(D2 + -5D + 6) * y = 12x * e3x

Reorder the terms:
(6 + -5D + D2) * y = 12x * e3x

Reorder the terms for easier multiplication:
y(6 + -5D + D2) = 12x * e3x
(6 * y + -5D * y + D2 * y) = 12x * e3x
(6y + -5yD + yD2) = 12x * e3x

Multiply x * e3x
6y + -5yD + yD2 = 12e3x2

Solving
6y + -5yD + yD2 = 12e3x2

Solving for variable 'y'.

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

Reorder the terms:
-12e3x2 + 6y + -5yD + yD2 = 12e3x2 + -12e3x2

Combine like terms: 12e3x2 + -12e3x2 = 0
-12e3x2 + 6y + -5yD + yD2 = 0

The solution to this equation could not be determined.

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