What is the solution for y^{''}-10y^'+21y=192e^t ?

The solution for y^{''}-10y^'+21y=192e^t is y=c_{1}e^{7t}+c_{2}e^{3t}+16e^t

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y^{''}-10y^'+21y=192e^t

y^{^{''}} - 10 y^{^{'}} + 21 y = 192 e^{t}

y = c_{1} e^{7 t} + c_{2} e^{3 t} + 16 e^{t}

Solution steps

y^{''} (t) - 10 y^{'} (t) + 21 y = 192 e^{t}

Solve linear ODE:

y = c_{1} e^{7 t} + c_{2} e^{3 t} + 16 e^{t}

y = c_{1} e^{7 t} + c_{2} e^{3 t} + 16 e^{t}

y^{^{''}} - 6 y + 10 y = 10 x^{2}

y^{^{''}} + y = - 3 x - 2

y^{^{''}} + 14 y^{^{'}} + 49 y = x^{- 3} e^{- 7 x}

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

y^{^{''}} - y = a x e^{- x}, y (0) = \frac{1}{4}, y^{^{'}} (0) = 0

What is the solution for y^{''}-10y^'+21y=192e^t ?
The solution for y^{''}-10y^'+21y=192e^t is y=c_{1}e^{7t}+c_{2}e^{3t}+16e^t