What is the solution for y^{''}-2y=x+1 ?

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

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y^{''}-2y=x+1

y^{^{''}} - 2 y = x + 1

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

Solution steps

y^{''} (x) - 2 y = x + 1

Solve linear ODE:

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

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

y^{^{''}} + (y^{^{'}}) 2 + 9 = 0

y^{^{''}} - y^{^{'}} = t, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + y = tan (2 t)

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

y^{^{''}} + 3 y^{^{'}} + 5 y = sin (t), y^{^{'}} (0) = 0, y (0) = 1

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