What is the solution for -21y+4y^'+y^{''}=t+1 ?

The solution for -21y+4y^'+y^{''}=t+1 is y=c_{1}e^{3t}+c_{2}e^{-7t}-t/(21)-25/441

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-21y+4y^'+y^{''}=t+1

- 21 y + 4 y^{^{'}} + y^{^{''}} = t + 1

y = c_{1} e^{3 t} + c_{2} e^{- 7 t} - \frac{t}{21} - \frac{25}{441}

Solution steps

- 21 y + 4 y^{'} (t) + y^{''} (t) = t + 1

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} e^{- 7 t} - \frac{t}{21} - \frac{25}{441}

y = c_{1} e^{3 t} + c_{2} e^{- 7 t} - \frac{t}{21} - \frac{25}{441}

y^{^{''}} + 14 y^{^{'}} + 50 y = 6 e^{- 7 t} cos (t)

y, d (y) = 7 (2)^{y}

y^{^{''}} + 4 y^{^{'}} + 5 y = 1 - 5 x + 8 (cos (x) - sin (x))

4 x^{^{''}} - 4 x^{^{'}} + x = \frac{8}{t ^{2}} e^{\frac{t}{2}}

- y^{^{''}} + 2 y^{^{'}} + 3 y = 1

What is the solution for -21y+4y^'+y^{''}=t+1 ?
The solution for -21y+4y^'+y^{''}=t+1 is y=c_{1}e^{3t}+c_{2}e^{-7t}-t/(21)-25/441