What is the solution for 2(d^2y)/(dt^2)+20(dy)/(dt)+50=8*(t) ?

The solution for 2(d^2y)/(dt^2)+20(dy)/(dt)+50=8*(t) is y=c_{1}+c_{2}e^{-10t}+(t^2)/5-(127t)/(50)

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2(d^2y)/(dt^2)+20(dy)/(dt)+50=8*(t)

2 \frac{d ^{2} y}{d t ^{2}} + 20 \frac{d y}{d t} + 50 = 8 \cdot (t)

y = c_{1} + c_{2} e^{- 10 t} + \frac{t ^{2}}{5} - \frac{127 t}{50}

Solution steps

2 \frac{d ^{2} y}{d t ^{2}} + 20 \frac{d y}{d t} + 50 = 8 \cdot (t)

Solve linear ODE:

y = c_{1} + c_{2} e^{- 10 t} + \frac{t ^{2}}{5} - \frac{127 t}{50}

y = c_{1} + c_{2} e^{- 10 t} + \frac{t ^{2}}{5} - \frac{127 t}{50}

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

x^{^{''}} - 3 x^{^{'}} + 2 x = 2 sin (t) - 6 cos (t)

x^{^{''}} + 8 x^{^{'}} + 16 x = 10 sin (4 t)

y^{^{''}} - 7 y^{^{'}} + 12 y = 6 e^{x}

y^{^{''}} + 7 y^{^{'}} + 10 y = 3 x^{2} + x - 2

What is the solution for 2(d^2y)/(dt^2)+20(dy)/(dt)+50=8*(t) ?
The solution for 2(d^2y)/(dt^2)+20(dy)/(dt)+50=8*(t) is y=c_{1}+c_{2}e^{-10t}+(t^2)/5-(127t)/(50)