What is the solution for y^{''''}-14y^{'''}+49y^{''}=0 ?

The solution for y^{''''}-14y^{'''}+49y^{''}=0 is y=c_{1}+c_{2}t+c_{3}e^{7t}+c_{4}te^{7t}

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y^{''''}-14y^{'''}+49y^{''}=0

y^{^{''''}} - 14 y^{^{'''}} + 49 y^{^{''}} = 0

y = c_{1} + c_{2} t + c_{3} e^{7 t} + c_{4} t e^{7 t}

Solution steps

y^{(4)} (t) - 14 y^{'''} (t) + 49 y^{''} (t) = 0

Solve linear ODE:

y = c_{1} + c_{2} t + c_{3} e^{7 t} + c_{4} t e^{7 t}

y = c_{1} + c_{2} t + c_{3} e^{7 t} + c_{4} t e^{7 t}

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

y^{^{''}} - 12 y^{^{'}} + 45 y = 0

x^{^{''}} + 3 x^{^{'}} + 4 x = 0

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

y^{^{''}} - 10 y^{^{'}} + 16 y = 0

What is the solution for y^{''''}-14y^{'''}+49y^{''}=0 ?
The solution for y^{''''}-14y^{'''}+49y^{''}=0 is y=c_{1}+c_{2}t+c_{3}e^{7t}+c_{4}te^{7t}