What is the solution for y^{''}-8y^'=5t ?

The solution for y^{''}-8y^'=5t is y=c_{1}e^{8t}+c_{2}-(5t^2)/(16)-(5t)/(64)

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y^{''}-8y^'=5t

y^{^{''}} - 8 y^{^{'}} = 5 t

y = c_{1} e^{8 t} + c_{2} - \frac{5 t ^{2}}{16} - \frac{5 t}{64}

Solution steps

y^{''} (t) - 8 y^{'} (t) = 5 t

Solve linear ODE:

y = c_{1} e^{8 t} + c_{2} - \frac{5 t ^{2}}{16} - \frac{5 t}{64}

y = c_{1} e^{8 t} + c_{2} - \frac{5 t ^{2}}{16} - \frac{5 t}{64}

y^{^{''}} + 4 y^{^{'}} + 4 y = 12 t + 16, y (0) = 3, y^{^{'}} (0) = - 4

\frac{d}{d x} (\frac{2 ^{0}}{3 ^{1} + 0})

n \to \infty lim (n)

y^{^{'}} - 2 y = 0, y (0) = 2

f (x) = cos (sin (5) x^{3})

What is the solution for y^{''}-8y^'=5t ?
The solution for y^{''}-8y^'=5t is y=c_{1}e^{8t}+c_{2}-(5t^2)/(16)-(5t)/(64)