What is the solution for y^{''}-10y^'+9y=5t,y(0)=-1 ?

The solution for y^{''}-10y^'+9y=5t,y(0)=-1 is y=(-c_{2}-131/81)e^{9t}+c_{2}e^t+(5t)/9+50/81

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y^{''}-10y^'+9y=5t,y(0)=-1

y^{^{''}} - 10 y^{^{'}} + 9 y = 5 t, y (0) = - 1

y = (- c_{2} - \frac{131}{81}) e^{9 t} + c_{2} e^{t} + \frac{5 t}{9} + \frac{50}{81}

Solution steps

y^{''} (t) - 10 y^{'} (t) + 9 y = 5 t

Solve linear ODE:

y = (- c_{2} - \frac{131}{81}) e^{9 t} + c_{2} e^{t} + \frac{5 t}{9} + \frac{50}{81}

y = (- c_{2} - \frac{131}{81}) e^{9 t} + c_{2} e^{t} + \frac{5 t}{9} + \frac{50}{81}

y^{^{''}} + 4 y^{^{'}} + 5 y = 15 t

y^{^{''}} - y^{^{'}} = 5 sin (2 t), y (0) = 0, y^{^{'}} (0) = 1

\frac{d ^{2} y}{d x ^{2}} + 9 y = sin (3 x) sec^{2} (3 x)

y^{^{''}} + 5 y^{^{'}} + 6 y = sin (t) - cos (2 t)

y^{^{''}} + 7 y^{^{'}} + 6 y = e^{2 t}

What is the solution for y^{''}-10y^'+9y=5t,y(0)=-1 ?
The solution for y^{''}-10y^'+9y=5t,y(0)=-1 is y=(-c_{2}-131/81)e^{9t}+c_{2}e^t+(5t)/9+50/81