What is the solution for y^{''''}-5y^{'''}+9y^{''}-7y^'+2y=0 ?

The solution for y^{''''}-5y^{'''}+9y^{''}-7y^'+2y=0 is y=c_{1}e^{2t}+c_{2}e^t+c_{3}te^t+c_{4}t^2e^t

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y^{''''}-5y^{'''}+9y^{''}-7y^'+2y=0

y^{^{''''}} - 5 y^{^{'''}} + 9 y^{^{''}} - 7 y^{^{'}} + 2 y = 0

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

Solution steps

y^{(4)} (t) - 5 y^{'''} (t) + 9 y^{''} (t) - 7 y^{'} (t) + 2 y = 0

Solve linear ODE:

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

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

4 y^{^{''}} - 12 y^{^{'}} + 5 y = 0

y^{^{'''}} + 6 y^{^{''}} - 11 y^{^{'}} - 116 y = 0

25 y^{^{''}} + 20 y^{^{'}} + 4 y = 0

4 \frac{d ^{2} y}{d x ^{2}} + 3 \frac{d y}{d x} - 10 y = 0

(4 D^{2} - 4 D + 5) y = 0

What is the solution for y^{''''}-5y^{'''}+9y^{''}-7y^'+2y=0 ?
The solution for y^{''''}-5y^{'''}+9y^{''}-7y^'+2y=0 is y=c_{1}e^{2t}+c_{2}e^t+c_{3}te^t+c_{4}t^2e^t