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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

10 6 x^{9} + 9 x^{6}

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

\frac{\partial}{\partial y} (x e^{y} - y e^{x})

\frac{\partial}{\partial x} (e^{x} - x^{2} arctan (x))

\frac{6 ( t + 1 ) d y}{d t} - 5 y = 5 t, y (0) = 4

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