What is the solution for y^{''}-14y^'+49y=2te^{7t} ?

The solution for y^{''}-14y^'+49y=2te^{7t} is y=c_{1}e^{7t}+c_{2}te^{7t}+(e^{7t}t^3)/3

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y^{''}-14y^'+49y=2te^{7t}

y^{^{''}} - 14 y^{^{'}} + 49 y = 2 t e^{7 t}

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

Solution steps

y^{''} (t) - 14 y^{'} (t) + 49 y = 2 t e^{7 t}

Solve linear ODE:

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

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

What is the solution for y^{''}-14y^'+49y=2te^{7t} ?
The solution for y^{''}-14y^'+49y=2te^{7t} is y=c_{1}e^{7t}+c_{2}te^{7t}+(e^{7t}t^3)/3