What is the solution for y^{''}+12y^'+36y=0,y^'(0)=0,y(0)=5 ?

The solution for y^{''}+12y^'+36y=0,y^'(0)=0,y(0)=5 is y=5e^{-6t}+30e^{-6t}t

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y^{''}+12y^'+36y=0,y^'(0)=0,y(0)=5

y^{^{''}} + 12 y^{^{'}} + 36 y = 0, y^{^{'}} (0) = 0, y (0) = 5

y = 5 e^{- 6 t} + 30 e^{- 6 t} t

Solution steps

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

Solve linear ODE:

y = 5 e^{- 6 t} + 30 e^{- 6 t} t

y = 5 e^{- 6 t} + 30 e^{- 6 t} t

What is the solution for y^{''}+12y^'+36y=0,y^'(0)=0,y(0)=5 ?
The solution for y^{''}+12y^'+36y=0,y^'(0)=0,y(0)=5 is y=5e^{-6t}+30e^{-6t}t