What is the solution for y^{''}-6y^'+9y=0,y(0)=1,y^'(0)=2 ?

The solution for y^{''}-6y^'+9y=0,y(0)=1,y^'(0)=2 is y=e^{3t}-e^{3t}t

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y^{''}-6y^'+9y=0,y(0)=1,y^'(0)=2

y^{^{''}} - 6 y^{^{'}} + 9 y = 0, y (0) = 1, y^{^{'}} (0) = 2

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{'''}} = y^{^{'}}

9 y^{^{''}} - 12 y^{^{'}} + 4 y = 0, y (0) = 1, y^{^{'}} (0) = \frac{4}{3}

y^{^{''}} - 4 y^{^{'}} + 4 y = 0, y^{1} (0) = e^{2 x}

y^{^{''}} + 4 y^{^{'}} + 3 y = 0, y (0) = 3, y^{^{'}} (0) = - 1

y^{^{'''}} - 5 y^{^{''}} + 2 y^{^{'}} + 8 y = 0

What is the solution for y^{''}-6y^'+9y=0,y(0)=1,y^'(0)=2 ?
The solution for y^{''}-6y^'+9y=0,y(0)=1,y^'(0)=2 is y=e^{3t}-e^{3t}t