What is the solution for y^{'''}-15y^{''}+62y^'-72y=0 ?

The solution for y^{'''}-15y^{''}+62y^'-72y=0 is y=c_{1}e^{2t}+c_{2}e^{4t}+c_{3}e^{9t}

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y^{'''}-15y^{''}+62y^'-72y=0

y^{^{'''}} - 15 y^{^{''}} + 62 y^{^{'}} - 72 y = 0

y = c_{1} e^{2 t} + c_{2} e^{4 t} + c_{3} e^{9 t}

Solution steps

y^{'''} (t) - 15 y^{''} (t) + 62 y^{'} (t) - 72 y = 0

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} e^{4 t} + c_{3} e^{9 t}

y = c_{1} e^{2 t} + c_{2} e^{4 t} + c_{3} e^{9 t}

y^{^{''}} + 2 y^{^{'}} = - y

y^{^{''}} + y = 0, y^{^{'}} (0) = - 5

y^{^{''}} + y^{^{'}} = 0, y (\frac{π}{3}) = 0, y^{^{'}} (\frac{π}{3}) = 2

y^{^{''}} - 4 y^{^{'}} + 4 y = 0, y (0) = 3

y^{^{''}} - 4 y^{^{'}} + 4 y = 0, y (0) = 0

What is the solution for y^{'''}-15y^{''}+62y^'-72y=0 ?
The solution for y^{'''}-15y^{''}+62y^'-72y=0 is y=c_{1}e^{2t}+c_{2}e^{4t}+c_{3}e^{9t}