What is the solution for y^{'''}-11y^{''}+35y^'-25y=0 ?

The solution for y^{'''}-11y^{''}+35y^'-25y=0 is y=c_{1}e^t+c_{2}e^{5t}+c_{3}te^{5t}

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y^{'''}-11y^{''}+35y^'-25y=0

y^{^{'''}} - 11 y^{^{''}} + 35 y^{^{'}} - 25 y = 0

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

Solution steps

y^{'''} (t) - 11 y^{''} (t) + 35 y^{'} (t) - 25 y = 0

Solve linear ODE:

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

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

y^{^{''''}} - 7 y^{^{'''}} - 49 y^{^{''}} + 343 y^{^{'}} = 0

y^{^{''}} + 18 y^{^{'}} + 82 y = 0, y (0) = 1, y^{^{'}} (0) = 0

2 x^{^{''}} + 8 x^{^{'}} + 10 x = 0

0.2 q^{^{''}} + 5 q^{^{'}} + 500 q = 0

x^{^{''}} + 6 x^{^{'}} + 5 x = 0, x^{^{'}} (0) = 1, x (0) = 2

What is the solution for y^{'''}-11y^{''}+35y^'-25y=0 ?
The solution for y^{'''}-11y^{''}+35y^'-25y=0 is y=c_{1}e^t+c_{2}e^{5t}+c_{3}te^{5t}