What is the solution for y^{''}-2y^'=2t ?

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

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y^{''}-2y^'=2t

y^{^{''}} - 2 y^{^{'}} = 2 t

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

Solution steps

y^{''} (t) - 2 y^{'} (t) = 2 t

Solve linear ODE:

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

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

x \to 3 + lim (\frac{x ^{2} + x}{x - 3})

cos (t + \frac{π}{4})

\int (3 y + 7) d y

\frac{5}{s + 2}

x^{2 x}

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