What is the solution for (d^4-7d^3+18d^2-20d+8)y=0 ?

The solution for (d^4-7d^3+18d^2-20d+8)y=0 is y=c_{1}e^x+c_{2}e^{2x}+c_{3}xe^{2x}+c_{4}x^2e^{2x}

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(d^4-7d^3+18d^2-20d+8)y=0

(d^{4} - 7 d^{3} + 18 d^{2} - 20 d + 8) y = 0

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

Solution steps

(d^{4} - 7 d^{3} + 18 d^{2} - 20 d + 8) y = 0

Solve linear ODE:

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

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

(d^{3} - d^{2}) y = 0

y^{^{''}} + 5 y^{^{'}} + 6 y = 0, y (0) = 2, y^{^{'}} (0) = 3

8 y^{^{''}} - 6 y^{^{'}} - 5 y = 0

y^{^{'''}} - 2 y^{^{''}} + 4 y^{^{'}} - 8 y = 0

(d^{4} - 8 d) y = 0

What is the solution for (d^4-7d^3+18d^2-20d+8)y=0 ?
The solution for (d^4-7d^3+18d^2-20d+8)y=0 is y=c_{1}e^x+c_{2}e^{2x}+c_{3}xe^{2x}+c_{4}x^2e^{2x}