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

The solution for y^{''}+6y^'+5y=2x is y=c_{1}e^{-x}+c_{2}e^{-5x}+(2x)/5-12/25

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

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

y = c_{1} e^{- x} + c_{2} e^{- 5 x} + \frac{2 x}{5} - \frac{12}{25}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 5 x} + \frac{2 x}{5} - \frac{12}{25}

y = c_{1} e^{- x} + c_{2} e^{- 5 x} + \frac{2 x}{5} - \frac{12}{25}

f (x) = 3 x^{\frac{1}{2}} + x^{\frac{3}{2}}, at x = 16

\int \frac{2}{x ( ln ( x ) ) ^{2}} d x

\frac{x ^{2}}{( 2 + x )}

y^{^{''}} - 8 y^{^{'}} - 17 y = 0

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

What is the solution for y^{''}+6y^'+5y=2x ?
The solution for y^{''}+6y^'+5y=2x is y=c_{1}e^{-x}+c_{2}e^{-5x}+(2x)/5-12/25