What is the solution for 36y^{''}+132y^'+121y=0,y(0)=5,y^'(0)=5 ?

The solution for 36y^{''}+132y^'+121y=0,y(0)=5,y^'(0)=5 is y=5e^{-(11t)/6}+(85e^{-(11t)/6}t)/(6)

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36y^{''}+132y^'+121y=0,y(0)=5,y^'(0)=5

36 y^{^{''}} + 132 y^{^{'}} + 121 y = 0, y (0) = 5, y^{^{'}} (0) = 5

y = 5 e^{- \frac{11 t}{6}} + \frac{85 e ^{- \frac{11 t}{6}} t}{6}

Solution steps

36 y^{''} (t) + 132 y^{'} (t) + 121 y = 0

Solve linear ODE:

y = 5 e^{- \frac{11 t}{6}} + \frac{85 e ^{- \frac{11 t}{6}} t}{6}

y = 5 e^{- \frac{11 t}{6}} + \frac{85 e ^{- \frac{11 t}{6}} t}{6}

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

y^{^{''}} + 2 y^{^{'}} + 2 y = 0, y (\frac{π}{4}) = 0, y^{^{'}} (\frac{π}{4}) = - 2

y^{^{'''}} + 19 y^{^{''}} - 14 y^{^{'}} - 266 y = 0

40 y^{^{''}} - a y^{^{'}} + 4000 y = 0

\frac{1}{8} y^{^{''}} + 4 y^{^{'}} + 28 y = 0

What is the solution for 36y^{''}+132y^'+121y=0,y(0)=5,y^'(0)=5 ?
The solution for 36y^{''}+132y^'+121y=0,y(0)=5,y^'(0)=5 is y=5e^{-(11t)/6}+(85e^{-(11t)/6}t)/(6)