What is the solution for y^{''}-10y^'+9y=5 ?

The solution for y^{''}-10y^'+9y=5 is y=c_{1}e^{9t}+c_{2}e^t+5/9

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y^{''}-10y^'+9y=5

y^{^{''}} - 10 y^{^{'}} + 9 y = 5

y = c_{1} e^{9 t} + c_{2} e^{t} + \frac{5}{9}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{9 t} + c_{2} e^{t} + \frac{5}{9}

y = c_{1} e^{9 t} + c_{2} e^{t} + \frac{5}{9}

y^{^{''}} - 8 y^{^{'}} + 20 y = 200 x^{2} - 78 x e^{x}

y^{^{''}} + y^{^{'}} - 12 y = 2 cos (t)

D^{2} (D - 1) y = 8 e^{2 x}

x^{^{''}} - x^{^{'}} - 6 x = 2 e^{4 t}

y^{^{''}} + a y = b

What is the solution for y^{''}-10y^'+9y=5 ?
The solution for y^{''}-10y^'+9y=5 is y=c_{1}e^{9t}+c_{2}e^t+5/9