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

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

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

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

y = e^{3 t} - 2 e^{3 t} t

Solution steps

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

Solve linear ODE:

y = e^{3 t} - 2 e^{3 t} t

y = e^{3 t} - 2 e^{3 t} t

y^{^{''}} - 6 y^{^{'}} + 9 y = 0, y (0) = 1, y^{^{'}} (0) = 4

y^{^{''}} - 8 y^{^{'}} + 16 y = 0, y (0) = 7, y^{^{'}} (0) = 0

\frac{17}{160} x^{^{''}} + 0.4 x^{^{'}} + 2 x = 0

y^{^{'''}} + 9 y^{^{'}} = 0, y (0) = - 21

y^{^{'}} + 18 y^{^{''}} + 81 y = 0

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