What is the solution for 7y^{''}-20y^'+12y=8e^2 ?

The solution for 7y^{''}-20y^'+12y=8e^2 is y=c_{1}e^{2t}+c_{2}e^{(6t)/7}+(2e^2)/3

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7y^{''}-20y^'+12y=8e^2

7 y^{^{''}} - 20 y^{^{'}} + 12 y = 8 e^{2}

y = c_{1} e^{2 t} + c_{2} e^{\frac{6 t}{7}} + \frac{2 e ^{2}}{3}

Solution steps

7 y^{''} (t) - 20 y^{'} (t) + 12 y = 8 e^{2}

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} e^{\frac{6 t}{7}} + \frac{2 e ^{2}}{3}

y = c_{1} e^{2 t} + c_{2} e^{\frac{6 t}{7}} + \frac{2 e ^{2}}{3}

What is the solution for 7y^{''}-20y^'+12y=8e^2 ?
The solution for 7y^{''}-20y^'+12y=8e^2 is y=c_{1}e^{2t}+c_{2}e^{(6t)/7}+(2e^2)/3