What is the solution for (d^2y)/(dx^2)+(dy)/(dx)=sin(x) ?

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

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(d^2y)/(dx^2)+(dy)/(dx)=sin(x)

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 81 y = e^{9 x}

x^{^{''}} - 4 x^{^{'}} + 3 x = 2 e^{t} - 5 e^{2 t}

y^{^{''}} + 4 y = t^{2} + 7 e^{t}, y (0) = 0, y^{^{'}} (0) = 2

y^{^{''}} + y^{^{'}} = (3 t^{2} + 2 t) e^{t} + cos (\frac{t}{2})

y^{^{''}} + 5 y^{^{'}} - 6 y = 2 sin (4 x)

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