What is the solution for y^{''}+2y^'=2x+7-e-2x ?

The solution for y^{''}+2y^'=2x+7-e-2x is y=c_{1}+c_{2}e^{-2x}+((-e+7)x)/2

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y^{''}+2y^'=2x+7-e-2x

y^{^{''}} + 2 y^{^{'}} = 2 x + 7 - e - 2 x

y = c_{1} + c_{2} e^{- 2 x} + \frac{( - e + 7 ) x}{2}

Solution steps

y^{''} (x) + 2 y^{'} (x) = 2 x + 7 - e - 2 x

Solve linear ODE:

y = c_{1} + c_{2} e^{- 2 x} + \frac{( - e + 7 ) x}{2}

y = c_{1} + c_{2} e^{- 2 x} + \frac{( - e + 7 ) x}{2}

\int sin (2 x) cos^{4} (2 x) d x

d er i v a t i v e f (x) = (7 x + 6)^{2}

y^{^{''}} = sin (x)

x (\frac{d y}{d x}) - y = (\frac{x ^{3}}{y}) e^{\frac{y}{x}}

x \to 0 lim (\frac{e ^{∣ x ∣} - 1}{x})

What is the solution for y^{''}+2y^'=2x+7-e-2x ?
The solution for y^{''}+2y^'=2x+7-e-2x is y=c_{1}+c_{2}e^{-2x}+((-e+7)x)/2