What is the solution for y^{''''}-10y^{'''}+25y^{''}=0 ?

The solution for y^{''''}-10y^{'''}+25y^{''}=0 is y=c_{1}+c_{2}t+c_{3}e^{5t}+c_{4}te^{5t}

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y^{''''}-10y^{'''}+25y^{''}=0

y^{^{''''}} - 10 y^{^{'''}} + 25 y^{^{''}} = 0

y = c_{1} + c_{2} t + c_{3} e^{5 t} + c_{4} t e^{5 t}

Solution steps

y^{(4)} (t) - 10 y^{'''} (t) + 25 y^{''} (t) = 0

Solve linear ODE:

y = c_{1} + c_{2} t + c_{3} e^{5 t} + c_{4} t e^{5 t}

y = c_{1} + c_{2} t + c_{3} e^{5 t} + c_{4} t e^{5 t}

y^{^{''}} + 9 y^{^{'}} + 20 y = 0

(4 D^{5} - 23 D^{3} - 33 D^{2} - 17 D - 3) y = 0

\frac{d ^{2} x}{d t ^{2}} + 5 \frac{d x}{d t} + 4 x = 0

y^{^{''}} - 7 y^{^{'}} = 0

y^{^{''}} + k y = 0

What is the solution for y^{''''}-10y^{'''}+25y^{''}=0 ?
The solution for y^{''''}-10y^{'''}+25y^{''}=0 is y=c_{1}+c_{2}t+c_{3}e^{5t}+c_{4}te^{5t}