What is the solution for y^{''}-4y^'+4y=0,y(0)=3,y^'(0)=0 ?

The solution for y^{''}-4y^'+4y=0,y(0)=3,y^'(0)=0 is y=3e^{2t}-6e^{2t}t

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

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

y = 3 e^{2 t} - 6 e^{2 t} t

Solution steps

y^{''} (t) - 4 y^{'} (t) + 4 y = 0

Solve linear ODE:

y = 3 e^{2 t} - 6 e^{2 t} t

y = 3 e^{2 t} - 6 e^{2 t} t

4 x^{^{''}} + x^{^{'}} + 7 x = 0

y^{^{''}} + 0.025 \cdot y + 0.1 y^{^{'}} = 0

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

y^{^{''}} + 16 y = 0, y^{^{'}} (0) = - 2, y (0) = 2

y^{^{''}} - 4 y = 0, y (0) = 0, y^{^{'}} (0) = 5

What is the solution for y^{''}-4y^'+4y=0,y(0)=3,y^'(0)=0 ?
The solution for y^{''}-4y^'+4y=0,y(0)=3,y^'(0)=0 is y=3e^{2t}-6e^{2t}t