What is the solution for x^{''}+5x^'+6x=10 ?

The solution for x^{''}+5x^'+6x=10 is x=c_{1}e^{-2t}+c_{2}e^{-3t}+5/3

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x^{''}+5x^'+6x=10

x^{^{''}} + 5 x^{^{'}} + 6 x = 10

x = c_{1} e^{- 2 t} + c_{2} e^{- 3 t} + \frac{5}{3}

Solution steps

x^{''} (t) + 5 x^{'} (t) + 6 x = 10

Solve linear ODE:

x = c_{1} e^{- 2 t} + c_{2} e^{- 3 t} + \frac{5}{3}

x = c_{1} e^{- 2 t} + c_{2} e^{- 3 t} + \frac{5}{3}

y^{^{''}} - 7 y^{^{'}} + 9 y = x, y^{1} (0) = e x

y^{^{''}} - 8 y + 20 y = 100 x^{2} - 26 x e^{x}

y^{^{''}} - 4 y^{^{'}} + y = (- 3 x + 4) sin (x)

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

y^{^{''}} + 2 y^{^{'}} - 8 y = 8 x^{2} - 3, y (0) = - 1, y^{^{'}} (0) = - 3

What is the solution for x^{''}+5x^'+6x=10 ?
The solution for x^{''}+5x^'+6x=10 is x=c_{1}e^{-2t}+c_{2}e^{-3t}+5/3