What is the solution for y^{''}+9y^'=0,y(0)=3,y^'(0)=-45 ?

The solution for y^{''}+9y^'=0,y(0)=3,y^'(0)=-45 is y=5e^{-9t}-2

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y^{''}+9y^'=0,y(0)=3,y^'(0)=-45

y^{^{''}} + 9 y^{^{'}} = 0, y (0) = 3, y^{^{'}} (0) = - 45

y = 5 e^{- 9 t} - 2

Solution steps

y^{''} (t) + 9 y^{'} (t) = 0

Solve linear ODE:

y = 5 e^{- 9 t} - 2

y = 5 e^{- 9 t} - 2

y^{^{''}} + \frac{33}{6} y^{^{'}} + 128 y = 0

15 y^{^{''}} - 16 y^{^{'}} - 7 y = 0

y^{^{''}} - 11 y^{^{'}} - 42 y = 0

y^{^{''}} - 4 \cdot y = 0

y^{^{''}} + y^{^{'}} + \frac{y}{4} = 0, y (0) = 0, y^{^{'}} (0) = 7

What is the solution for y^{''}+9y^'=0,y(0)=3,y^'(0)=-45 ?
The solution for y^{''}+9y^'=0,y(0)=3,y^'(0)=-45 is y=5e^{-9t}-2