What is the solution for y^{''}-6y^'+9y=0,y(0)=-3,y^'(0)=5 ?

The solution for y^{''}-6y^'+9y=0,y(0)=-3,y^'(0)=5 is y=-3e^{3t}+14e^{3t}t

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y^{''}-6y^'+9y=0,y(0)=-3,y^'(0)=5

y^{^{''}} - 6 y^{^{'}} + 9 y = 0, y (0) = - 3, y^{^{'}} (0) = 5

y = - 3 e^{3 t} + 14 e^{3 t} t

Solution steps

y^{''} (t) - 6 y^{'} (t) + 9 y = 0

Solve linear ODE:

y = - 3 e^{3 t} + 14 e^{3 t} t

y = - 3 e^{3 t} + 14 e^{3 t} t

\frac{d y}{d x} = (x + 1)^{2}

\int_{1}^{3} (x + 2) (x - 1)^{5} d x

\frac{d}{d x} (\frac{- x ^{2} - 4 x - 1}{4 x - 3})

\int e^{x^{3} + 1} x^{2} d x

\frac{d}{d x} (ln (e^{3 x} + e^{- 3 x}))

What is the solution for y^{''}-6y^'+9y=0,y(0)=-3,y^'(0)=5 ?
The solution for y^{''}-6y^'+9y=0,y(0)=-3,y^'(0)=5 is y=-3e^{3t}+14e^{3t}t