What is the solution for y^{'''}-15y^{''}+72y^'-108y=0 ?

The solution for y^{'''}-15y^{''}+72y^'-108y=0 is y=c_{1}e^{3t}+c_{2}e^{6t}+c_{3}te^{6t}

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y^{'''}-15y^{''}+72y^'-108y=0

y^{^{'''}} - 15 y^{^{''}} + 72 y^{^{'}} - 108 y = 0

y = c_{1} e^{3 t} + c_{2} e^{6 t} + c_{3} t e^{6 t}

Solution steps

y^{'''} (t) - 15 y^{''} (t) + 72 y^{'} (t) - 108 y = 0

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} e^{6 t} + c_{3} t e^{6 t}

y = c_{1} e^{3 t} + c_{2} e^{6 t} + c_{3} t e^{6 t}

\frac{1}{2} \frac{d ^{2} y}{d x ^{2}} + 6 \frac{d y}{d x} + 26 y = 0

y^{^{''}} - 2 y^{^{'}} - 3 y = 0, y (4) = - 17

y^{^{'''}} + (- 7) y^{^{''}} + 8 y^{^{'}} + 16 y = 0

y^{^{''}} + 2 y^{^{'}} + y = 0, y (1) = - x e^{x}

y^{^{''}} + a^{2} b^{2} y = 0

What is the solution for y^{'''}-15y^{''}+72y^'-108y=0 ?
The solution for y^{'''}-15y^{''}+72y^'-108y=0 is y=c_{1}e^{3t}+c_{2}e^{6t}+c_{3}te^{6t}