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}

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

y^{^{''}} + 4 y^{^{'}} - 5 y = 0, y^{^{'}} (ln (2)) = 3, y (0) = 33

\frac{d ^{2} x}{d t ^{2}} - 49 x = 0, x = 2

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}