What is the solution for y^{''}-6y^'=36t,y(0)=6,y^'(0)=0 ?

The solution for y^{''}-6y^'=36t,y(0)=6,y^'(0)=0 is y=(6-35/6)e^{6t}+35/6-3t^2-t

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y^{''}-6y^'=36t,y(0)=6,y^'(0)=0

y^{^{''}} - 6 y^{^{'}} = 36 t, y (0) = 6, y^{^{'}} (0) = 0

y = (6 - \frac{35}{6}) e^{6 t} + \frac{35}{6} - 3 t^{2} - t

Solution steps

y^{''} (t) - 6 y^{'} (t) = 36 t

Solve linear ODE:

y = (6 - \frac{35}{6}) e^{6 t} + \frac{35}{6} - 3 t^{2} - t

y = (6 - \frac{35}{6}) e^{6 t} + \frac{35}{6} - 3 t^{2} - t

\int_{0}^{8} x^{3} e^{x} d x

f (x) = 3 x^{\frac{1}{2}} + x^{- \frac{3}{2}}

\frac{x - 4}{x + 4}

y = x^{2} - 6 x + 9, (3, 0)

x \to \infty lim (x^{2} - 2 x)

What is the solution for y^{''}-6y^'=36t,y(0)=6,y^'(0)=0 ?
The solution for y^{''}-6y^'=36t,y(0)=6,y^'(0)=0 is y=(6-35/6)e^{6t}+35/6-3t^2-t