What is the solution for y^{''}-4y^'+4y=0,y(0)=5,y^'(0)= 53/5 ?

The solution for y^{''}-4y^'+4y=0,y(0)=5,y^'(0)= 53/5 is y=5e^{2t}+(3e^{2t}t)/5

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y^{''}-4y^'+4y=0,y(0)=5,y^'(0)= 53/5

y^{^{''}} - 4 y^{^{'}} + 4 y = 0, y (0) = 5, y^{^{'}} (0) = \frac{53}{5}

y = 5 e^{2 t} + \frac{3 e ^{2 t} t}{5}

Solution steps

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

Solve linear ODE:

y = 5 e^{2 t} + \frac{3 e ^{2 t} t}{5}

y = 5 e^{2 t} + \frac{3 e ^{2 t} t}{5}

y^{^{''}} - 3 y^{^{'}} + 2 y = 0, y (0) = \frac{3}{5}, y^{^{'}} (0) = - \frac{1}{5}

\frac{d ^{4} y}{d x ^{4}} + 8 \frac{d ^{2} y}{d x ^{2}} + 6 y = 0

(D^{4} - D^{2}) y = 0

\frac{1}{2} x^{^{''}} + 3 x^{^{'}} + 4 x = 0, x (0) = 3, x^{^{'}} (0) = 0

y^{^{'''}} - 7 y^{^{''}} + 10 y = 0, y (0) = 7

What is the solution for y^{''}-4y^'+4y=0,y(0)=5,y^'(0)= 53/5 ?
The solution for y^{''}-4y^'+4y=0,y(0)=5,y^'(0)= 53/5 is y=5e^{2t}+(3e^{2t}t)/5