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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

8 y^{^{''}} - 25 y^{^{'}} + 3 y = 0

25 y^{^{''}} - 100 y^{^{'}} + 109 y = 0, y (0) = 9, y^{^{'}} (0) = 8

256 y^{^{''''}} = 81 y

3 y^{^{''}} + 15 y = 0

y^{^{''}} + (2 a - 5) y^{^{'}} + a (a - 5) y = 0

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