What is the solution for y^{''}-3y^'=9t,y(0)=3,y^'(0)=0 ?

The solution for y^{''}-3y^'=9t,y(0)=3,y^'(0)=0 is y=(3-8/3)e^{3t}+8/3-(3t^2)/2-t

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y^{''}-3y^'=9t,y(0)=3,y^'(0)=0

y^{^{''}} - 3 y^{^{'}} = 9 t, y (0) = 3, y^{^{'}} (0) = 0

y = (3 - \frac{8}{3}) e^{3 t} + \frac{8}{3} - \frac{3 t ^{2}}{2} - t

Solution steps

y^{''} (t) - 3 y^{'} (t) = 9 t

Solve linear ODE:

y = (3 - \frac{8}{3}) e^{3 t} + \frac{8}{3} - \frac{3 t ^{2}}{2} - t

y = (3 - \frac{8}{3}) e^{3 t} + \frac{8}{3} - \frac{3 t ^{2}}{2} - t

\frac{x}{y} + \frac{y}{x} = 3 πa b^{2}

\frac{( - 2 s - 1 )}{s + 1}

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

2 x - 1, at x = 5

\int ln (22 x) d x

What is the solution for y^{''}-3y^'=9t,y(0)=3,y^'(0)=0 ?
The solution for y^{''}-3y^'=9t,y(0)=3,y^'(0)=0 is y=(3-8/3)e^{3t}+8/3-(3t^2)/2-t