What is the solution for (d^2y)/(dt^2)-2(dy)/(dt)+y=5e^t ?

The solution for (d^2y)/(dt^2)-2(dy)/(dt)+y=5e^t is y=c_{1}e^t+c_{2}te^t+(5e^tt^2)/2

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(d^2y)/(dt^2)-2(dy)/(dt)+y=5e^t

\frac{d ^{2} y}{d t ^{2}} - 2 \frac{d y}{d t} + y = 5 e^{t}

y = c_{1} e^{t} + c_{2} t e^{t} + \frac{5 e ^{t} t ^{2}}{2}

Solution steps

\frac{d ^{2} y}{d t ^{2}} - 2 \frac{d y}{d t} + y = 5 e^{t}

Solve linear ODE:

y = c_{1} e^{t} + c_{2} t e^{t} + \frac{5 e ^{t} t ^{2}}{2}

y = c_{1} e^{t} + c_{2} t e^{t} + \frac{5 e ^{t} t ^{2}}{2}

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

y^{^{''}} + 4 y = 3, 2 sin (4 t) y (0) = 1

y^{^{''}} - y^{^{'}} - 6 y = x e^{x}

x^{^{''}} + 4 x = - t^{2}

y^{^{''}} + y = 5 sec^{3} (x)

What is the solution for (d^2y)/(dt^2)-2(dy)/(dt)+y=5e^t ?
The solution for (d^2y)/(dt^2)-2(dy)/(dt)+y=5e^t is y=c_{1}e^t+c_{2}te^t+(5e^tt^2)/2