What is the solution for 324y^{''}+396y^'+121y=0 ?

The solution for 324y^{''}+396y^'+121y=0 is y=c_{1}e^{-(11t)/(18)}+c_{2}e^{-(11t)/(18)}t

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324y^{''}+396y^'+121y=0

324 y^{^{''}} + 396 y^{^{'}} + 121 y = 0

y = c_{1} e^{- \frac{11 t}{18}} + c_{2} e^{- \frac{11 t}{18}} t

Solution steps

324 y^{''} (t) + 396 y^{'} (t) + 121 y = 0

Solve linear ODE:

y = c_{1} e^{- \frac{11 t}{18}} + c_{2} e^{- \frac{11 t}{18}} t

y = c_{1} e^{- \frac{11 t}{18}} + c_{2} e^{- \frac{11 t}{18}} t

y^{^{''}} - 144 y = 0

y^{^{''''}} + 4 y^{^{'''}} + 8 y^{^{''}} + 16 y^{^{'}} + 16 y = 0

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

y^{^{'''}} - 17 y^{^{''}} + 80 y^{^{'}} - 100 y = 0

2 y^{^{'''}} + 15 y^{^{''}} + 24 y^{^{'}} + 11 y = 0

What is the solution for 324y^{''}+396y^'+121y=0 ?
The solution for 324y^{''}+396y^'+121y=0 is y=c_{1}e^{-(11t)/(18)}+c_{2}e^{-(11t)/(18)}t