What is the solution for y^{''''}-36y^{'''}+324y^{''}=0 ?

The solution for y^{''''}-36y^{'''}+324y^{''}=0 is y=c_{1}+c_{2}t+c_{3}e^{18t}+c_{4}te^{18t}

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y^{''''}-36y^{'''}+324y^{''}=0

y^{^{''''}} - 36 y^{^{'''}} + 324 y^{^{''}} = 0

y = c_{1} + c_{2} t + c_{3} e^{18 t} + c_{4} t e^{18 t}

Solution steps

y^{(4)} (t) - 36 y^{'''} (t) + 324 y^{''} (t) = 0

Solve linear ODE:

y = c_{1} + c_{2} t + c_{3} e^{18 t} + c_{4} t e^{18 t}

y = c_{1} + c_{2} t + c_{3} e^{18 t} + c_{4} t e^{18 t}

x^{^{''}} + 9 x = 0, x (0) = 3, x^{^{'}} (0) = 4

y^{^{''}} - 7 y^{^{'}} + 2 y = 0

\frac{d ^{2} y}{d t ^{2}} + 7 \frac{d y}{d t} + k y = 0

y^{^{''}} - 4 y^{^{'}} + 5 y = 0, y (0) = - 1, y^{^{'}} (0) = 5

x, \frac{d ^{2} x}{d y ^{2}} + 0.1 x = 0

What is the solution for y^{''''}-36y^{'''}+324y^{''}=0 ?
The solution for y^{''''}-36y^{'''}+324y^{''}=0 is y=c_{1}+c_{2}t+c_{3}e^{18t}+c_{4}te^{18t}