What is the solution for (d^4-5d^3+5d^2+5d-6)y=0 ?

The solution for (d^4-5d^3+5d^2+5d-6)y=0 is y=c_{1}e^{-x}+c_{2}e^x+c_{3}e^{2x}+c_{4}e^{3x}

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(d^4-5d^3+5d^2+5d-6)y=0

(d^{4} - 5 d^{3} + 5 d^{2} + 5 d - 6) y = 0

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

Solution steps

(d^{4} - 5 d^{3} + 5 d^{2} + 5 d - 6) y = 0

Solve linear ODE:

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

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

14 y^{^{''''}} + 95 y^{^{''}} + 144 y = 0

y^{^{''}} = 5 y

5 \frac{d ^{2} x}{d t ^{2}} + 3 \frac{d x}{d t} + 6 x = 0, x (0) = 2

\frac{d ^{2} f}{d x ^{2}} = 2 f (x)

22 y^{^{''''}} + 29 y^{^{''}} + 9 y = 0

What is the solution for (d^4-5d^3+5d^2+5d-6)y=0 ?
The solution for (d^4-5d^3+5d^2+5d-6)y=0 is y=c_{1}e^{-x}+c_{2}e^x+c_{3}e^{2x}+c_{4}e^{3x}