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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

t^{2} y^{^{'}} + t y = y

n = 1 \sum \infty \frac{3}{n ^{2} + 3 n}

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

x \to 4 lim (\frac{x ^{2} - 1}{x - 4})

\frac{d}{d x} (- x^{- x})

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