What is the solution for y^{''}-4y^'+3y=2t ?

The solution for y^{''}-4y^'+3y=2t is y=c_{1}e^{3t}+c_{2}e^t+(2t)/3+8/9

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y^{''}-4y^'+3y=2t

y^{^{''}} - 4 y^{^{'}} + 3 y = 2 t

y = c_{1} e^{3 t} + c_{2} e^{t} + \frac{2 t}{3} + \frac{8}{9}

Solution steps

y^{''} (t) - 4 y^{'} (t) + 3 y = 2 t

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} e^{t} + \frac{2 t}{3} + \frac{8}{9}

y = c_{1} e^{3 t} + c_{2} e^{t} + \frac{2 t}{3} + \frac{8}{9}

What is the solution for y^{''}-4y^'+3y=2t ?
The solution for y^{''}-4y^'+3y=2t is y=c_{1}e^{3t}+c_{2}e^t+(2t)/3+8/9