What is the solution for y^{''}+5y^'+6y=2x ?

The solution for y^{''}+5y^'+6y=2x is y=c_{1}e^{-2x}+c_{2}e^{-3x}+x/3-5/18

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y^{''}+5y^'+6y=2x

y^{^{''}} + 5 y^{^{'}} + 6 y = 2 x

y = c_{1} e^{- 2 x} + c_{2} e^{- 3 x} + \frac{x}{3} - \frac{5}{18}

Solution steps

y^{''} (x) + 5 y^{'} (x) + 6 y = 2 x

Solve linear ODE:

y = c_{1} e^{- 2 x} + c_{2} e^{- 3 x} + \frac{x}{3} - \frac{5}{18}

y = c_{1} e^{- 2 x} + c_{2} e^{- 3 x} + \frac{x}{3} - \frac{5}{18}

\frac{d}{d x} (x^{3} \cdot sin^{2} (5 x))

x \to 1 lim (\frac{1}{1 - x})

\int (x + \frac{1}{x})^{2} (x - \frac{1}{x})^{2} - x + \frac{1}{x} d x

\frac{\partial}{\partial y} (arctan (x t))

\frac{\partial}{\partial x} (\frac{sin ( x )}{sin ( y )})

What is the solution for y^{''}+5y^'+6y=2x ?
The solution for y^{''}+5y^'+6y=2x is y=c_{1}e^{-2x}+c_{2}e^{-3x}+x/3-5/18