What is the solution for y^{''}-8y^'=64t,y(0)=8,y^'(0)=0 ?

The solution for y^{''}-8y^'=64t,y(0)=8,y^'(0)=0 is y=(8-63/8)e^{8t}+63/8-4t^2-t

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y^{''}-8y^'=64t,y(0)=8,y^'(0)=0

y^{^{''}} - 8 y^{^{'}} = 64 t, y (0) = 8, y^{^{'}} (0) = 0

y = (8 - \frac{63}{8}) e^{8 t} + \frac{63}{8} - 4 t^{2} - t

Solution steps

y^{''} (t) - 8 y^{'} (t) = 64 t

Solve linear ODE:

y = (8 - \frac{63}{8}) e^{8 t} + \frac{63}{8} - 4 t^{2} - t

y = (8 - \frac{63}{8}) e^{8 t} + \frac{63}{8} - 4 t^{2} - t

\int \frac{x ^{3}}{2 x + 1} d x

\frac{d}{d x} (ln (a x^{2} + b))

y \to 1 lim (85)

\frac{d}{d y} (2 e^{x y^{2}})

y^{^{'}} = 3 y + x

What is the solution for y^{''}-8y^'=64t,y(0)=8,y^'(0)=0 ?
The solution for y^{''}-8y^'=64t,y(0)=8,y^'(0)=0 is y=(8-63/8)e^{8t}+63/8-4t^2-t