What is the solution for y^{''}+12y^'+36y=0,y(0)=-5,y^'(0)=33 ?

The solution for y^{''}+12y^'+36y=0,y(0)=-5,y^'(0)=33 is y=-5e^{-6t}+3e^{-6t}t

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y^{''}+12y^'+36y=0,y(0)=-5,y^'(0)=33

y^{^{''}} + 12 y^{^{'}} + 36 y = 0, y (0) = - 5, y^{^{'}} (0) = 33

y = - 5 e^{- 6 t} + 3 e^{- 6 t} t

Solution steps

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

Solve linear ODE:

y = - 5 e^{- 6 t} + 3 e^{- 6 t} t

y = - 5 e^{- 6 t} + 3 e^{- 6 t} t

y^{^{''}} - 16 y = 0, y (0) = 3

2 y^{^{''}} - 5 y^{^{'}} - 3 y = 3 y

10000 y^{^{''}} - 81 y^{^{'}} = 0, y (0) = 8, y^{^{'}} (0) = 5

y^{^{''}} - 4 y^{^{'}} + 4 y = 0, y (0) = 8, y (1) = 0

\frac{d ^{2} y}{d x ^{2}} - \frac{11}{2} \frac{d y}{d x} + 6 y = 0

What is the solution for y^{''}+12y^'+36y=0,y(0)=-5,y^'(0)=33 ?
The solution for y^{''}+12y^'+36y=0,y(0)=-5,y^'(0)=33 is y=-5e^{-6t}+3e^{-6t}t