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

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

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

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

y = c_{1} e^{x} + c_{2} e^{- x} - x - 2 - \frac{1}{5} cos (2 x)

Solution steps

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- x} - x - 2 - \frac{1}{5} cos (2 x)

y = c_{1} e^{x} + c_{2} e^{- x} - x - 2 - \frac{1}{5} cos (2 x)

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 8 y = 3 cos (x)

3 y^{^{''}} + 3 y^{^{'}} - y = x^{2} e^{x}

x^{^{''}} + 2 x^{^{'}} + 2 x = cos (t)

\frac{d ^{2} y}{d x ^{2}} - 14 \frac{d y}{d x} + 49 y = 3 e^{7 x}

\frac{d ^{2} y}{d t ^{2}} - 5 \frac{d y}{d t} - 6 y = t + e^{- t}

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