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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + y^{^{'}} = 3 x^{2}

y^{^{''}} - 2 y^{^{'}} + 1 = e^{t} arctan (t)

y^{^{''}} - y^{^{'}} - 6 y = 17 cos (3 x)

y^{^{''}} + 3 y = x^{3} + 1

y^{^{''}} - 4 y^{^{'}} - 4 t + 4 = 0, y (0) = 2, y^{^{'}} (0) = 9

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