What is the solution for y^{''}-4y^'+4y=0,y(0)=5,y^'(0)=2 ?

The solution for y^{''}-4y^'+4y=0,y(0)=5,y^'(0)=2 is y=5e^{2t}-8e^{2t}t

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y^{''}-4y^'+4y=0,y(0)=5,y^'(0)=2

y^{^{''}} - 4 y^{^{'}} + 4 y = 0, y (0) = 5, y^{^{'}} (0) = 2

y = 5 e^{2 t} - 8 e^{2 t} t

Solution steps

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

Solve linear ODE:

y = 5 e^{2 t} - 8 e^{2 t} t

y = 5 e^{2 t} - 8 e^{2 t} t

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

4 y^{^{''}} - 36 y = 0

x^{^{''}} + 2 x^{^{'}} + (1 - k) x = 0

49 y^{^{''}} + 36 y = 0

100 y^{^{''}} + 60 y^{^{'}} + 90 y = 0, y (1) = 9, y^{^{'}} (1) = 2

What is the solution for y^{''}-4y^'+4y=0,y(0)=5,y^'(0)=2 ?
The solution for y^{''}-4y^'+4y=0,y(0)=5,y^'(0)=2 is y=5e^{2t}-8e^{2t}t