What is the solution for y^{''}+5y^'+6y=12 ?

The solution for y^{''}+5y^'+6y=12 is y=c_{1}e^{-2t}+c_{2}e^{-3t}+2

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y^{''}+5y^'+6y=12

y^{^{''}} + 5 y^{^{'}} + 6 y = 12

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

Solution steps

y^{''} (t) + 5 y^{'} (t) + 6 y = 12

Solve linear ODE:

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

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

f (x) = 2 x^{3} - 5 x^{2} + 6

\int_{- 1}^{1} x^{2} - 2 - e^{x} d x

\int_{0}^{π} sin (t) d t

y^{^{'}} = 2 x - y

\frac{d}{d x} (3^{x^{2} - x + 5})

What is the solution for y^{''}+5y^'+6y=12 ?
The solution for y^{''}+5y^'+6y=12 is y=c_{1}e^{-2t}+c_{2}e^{-3t}+2