What is the solution for y^{''}+12y^'+36y=0,y(0)=-1,y^'(0)=9 ?

The solution for y^{''}+12y^'+36y=0,y(0)=-1,y^'(0)=9 is y=-e^{-6t}+3e^{-6t}t

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y^{''}+12y^'+36y=0,y(0)=-1,y^'(0)=9

y^{^{''}} + 12 y^{^{'}} + 36 y = 0, y (0) = - 1, y^{^{'}} (0) = 9

y = - e^{- 6 t} + 3 e^{- 6 t} t

Solution steps

y^{''} (t) + 12 y^{'} (t) + 36 y = 0

Solve linear ODE:

y = - e^{- 6 t} + 3 e^{- 6 t} t

y = - e^{- 6 t} + 3 e^{- 6 t} t

x^{^{''}} + 3 x^{^{'}} + 3 x = 0

49 y^{^{''}} - 14 y^{^{'}} + y = 0

x^{^{''}} + 2 x^{^{'}} - 3 x = 0, x (0) = 2, x^{^{'}} (0) = 3

\frac{3}{4} \cdot x^{^{''}} + 36 x = 0, x^{^{'}} (0) = 0, x (0) = - 6

y^{^{''}} + 6 y^{^{'}} + 8 y = 0, y (0) = 0, y^{^{'}} (0) = - 5

What is the solution for y^{''}+12y^'+36y=0,y(0)=-1,y^'(0)=9 ?
The solution for y^{''}+12y^'+36y=0,y(0)=-1,y^'(0)=9 is y=-e^{-6t}+3e^{-6t}t