What is the solution for y^{''}-10y^'+21y=e^{7t} ?

The solution for y^{''}-10y^'+21y=e^{7t} is y=c_{1}e^{7t}+c_{2}e^{3t}+(e^{7t}t)/4

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y^{''}-10y^'+21y=e^{7t}

y^{^{''}} - 10 y^{^{'}} + 21 y = e^{7 t}

y = c_{1} e^{7 t} + c_{2} e^{3 t} + \frac{e ^{7 t} t}{4}

Solution steps

y^{''} (t) - 10 y^{'} (t) + 21 y = e^{7 t}

Solve linear ODE:

y = c_{1} e^{7 t} + c_{2} e^{3 t} + \frac{e ^{7 t} t}{4}

y = c_{1} e^{7 t} + c_{2} e^{3 t} + \frac{e ^{7 t} t}{4}

y^{^{''}} + 7 y^{^{'}} + 10 = x

y^{^{''}} - 9 y = (x^{2} - 2) \cdot sin (3 x)

y^{^{'''}} - 16 y^{^{'}} = t e^{- 4 t}

y^{^{''}} + 4 y = t^{2} + 6 e^{t}, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} + 4 y = t^{2} + 6 e^{t}, y (0) = 0, y^{^{'}} (0) = 3

What is the solution for y^{''}-10y^'+21y=e^{7t} ?
The solution for y^{''}-10y^'+21y=e^{7t} is y=c_{1}e^{7t}+c_{2}e^{3t}+(e^{7t}t)/4