What is the solution for y^{''}-4y^'+3y=0,y(0)= 3/5 ,y^'(0)= 1/5 ?

The solution for y^{''}-4y^'+3y=0,y(0)= 3/5 ,y^'(0)= 1/5 is y=(3/5-4/5)e^{3t}+4/5 e^t

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y^{''}-4y^'+3y=0,y(0)= 3/5 ,y^'(0)= 1/5

y^{^{''}} - 4 y^{^{'}} + 3 y = 0, y (0) = \frac{3}{5}, y^{^{'}} (0) = \frac{1}{5}

y = (\frac{3}{5} - \frac{4}{5}) e^{3 t} + \frac{4}{5} e^{t}

Solution steps

y^{''} (t) - 4 y^{'} (t) + 3 y = 0

Solve linear ODE:

y = (\frac{3}{5} - \frac{4}{5}) e^{3 t} + \frac{4}{5} e^{t}

y = (\frac{3}{5} - \frac{4}{5}) e^{3 t} + \frac{4}{5} e^{t}

What is the solution for y^{''}-4y^'+3y=0,y(0)= 3/5 ,y^'(0)= 1/5 ?
The solution for y^{''}-4y^'+3y=0,y(0)= 3/5 ,y^'(0)= 1/5 is y=(3/5-4/5)e^{3t}+4/5 e^t