What is the solution for (d^4-6d^3-12d^2+38d-21)y=0 ?

The solution for (d^4-6d^3-12d^2+38d-21)y=0 is y=c_{1}e^{-3x}+c_{2}e^{7x}+c_{3}e^x+c_{4}xe^x

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(d^4-6d^3-12d^2+38d-21)y=0

(d^{4} - 6 d^{3} - 12 d^{2} + 38 d - 21) y = 0

y = c_{1} e^{- 3 x} + c_{2} e^{7 x} + c_{3} e^{x} + c_{4} x e^{x}

Solution steps

(d^{4} - 6 d^{3} - 12 d^{2} + 38 d - 21) y = 0

Solve linear ODE:

y = c_{1} e^{- 3 x} + c_{2} e^{7 x} + c_{3} e^{x} + c_{4} x e^{x}

y = c_{1} e^{- 3 x} + c_{2} e^{7 x} + c_{3} e^{x} + c_{4} x e^{x}

What is the solution for (d^4-6d^3-12d^2+38d-21)y=0 ?
The solution for (d^4-6d^3-12d^2+38d-21)y=0 is y=c_{1}e^{-3x}+c_{2}e^{7x}+c_{3}e^x+c_{4}xe^x