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

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

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2y^{''}-y^'-y=6e^{-x/2}

2 y^{^{''}} - y^{^{'}} - y = 6 e^{- \frac{x}{2}}

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

Solution steps

2 y^{''} (x) - y^{'} (x) - y = 6 e^{- \frac{x}{2}}

Solve linear ODE:

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

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

\frac{d}{d x} (\frac{7}{x + 5})

\frac{d}{d x} (sin (4 x + 3))

y^{^{'}} = \frac{( x + y ) ^{2}}{2 x ^{2}}

f (x) = 3 x^{3} + 2 x^{2} + 1, at x = - 1

x \to - 2 - lim (\frac{- 3}{x + 2})

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