What is the solution for x^{''}-5x^'+6x=e^t ?

The solution for x^{''}-5x^'+6x=e^t is x=c_{1}e^{3t}+c_{2}e^{2t}+1/2 e^t

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x^{''}-5x^'+6x=e^t

x^{^{''}} - 5 x^{^{'}} + 6 x = e^{t}

x = c_{1} e^{3 t} + c_{2} e^{2 t} + \frac{1}{2} e^{t}

Solution steps

x^{''} (t) - 5 x^{'} (t) + 6 x = e^{t}

Solve linear ODE:

x = c_{1} e^{3 t} + c_{2} e^{2 t} + \frac{1}{2} e^{t}

x = c_{1} e^{3 t} + c_{2} e^{2 t} + \frac{1}{2} e^{t}

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What is the solution for x^{''}-5x^'+6x=e^t ?
The solution for x^{''}-5x^'+6x=e^t is x=c_{1}e^{3t}+c_{2}e^{2t}+1/2 e^t