What is the solution for y^{''}-6y^'+9y=0,y(0)=20,y^'(0)=0 ?

The solution for y^{''}-6y^'+9y=0,y(0)=20,y^'(0)=0 is y=20e^{3t}-60e^{3t}t

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y^{''}-6y^'+9y=0,y(0)=20,y^'(0)=0

y^{^{''}} - 6 y^{^{'}} + 9 y = 0, y (0) = 20, y^{^{'}} (0) = 0

y = 20 e^{3 t} - 60 e^{3 t} t

Solution steps

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

Solve linear ODE:

y = 20 e^{3 t} - 60 e^{3 t} t

y = 20 e^{3 t} - 60 e^{3 t} t

x^{^{''}} + 6 x^{^{'}} + 13 x = 0

c y^{^{''}} + ab y^{^{'}} = 0

3 y^{^{''}} + 35 y = 0, y (0) = 2, y^{^{'}} (0) = 9

(D^{3} + D^{2} - 2 D + 12) y = 0

y^{^{''}} + 3 y^{^{'}} + 2 y = 0, y (0) = 1, y^{^{'}} (0) = 3

What is the solution for y^{''}-6y^'+9y=0,y(0)=20,y^'(0)=0 ?
The solution for y^{''}-6y^'+9y=0,y(0)=20,y^'(0)=0 is y=20e^{3t}-60e^{3t}t