What is the solution for (xdy)/(dx)-(2dy)/(dx)-(x-2)sin(x)+y=0 ?

The solution for (xdy)/(dx)-(2dy)/(dx)-(x-2)sin(x)+y=0 is y=-cos(x)+(sin(x))/(x-2)+(c_{1})/(x-2)

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(xdy)/(dx)-(2dy)/(dx)-(x-2)sin(x)+y=0

\frac{x d y}{d x} - \frac{2 d y}{d x} - (x - 2) sin (x) + y = 0

y = - cos (x) + \frac{sin ( x )}{x - 2} + \frac{c _{1}}{x - 2}

Solution steps

\frac{x d y}{d x} - \frac{2 d y}{d x} - (x - 2) sin (x) + y = 0

Solve linear ODE:

y = - cos (x) + \frac{sin ( x )}{x - 2} + \frac{c _{1}}{x - 2}

y = - cos (x) + \frac{sin ( x )}{x - 2} + \frac{c _{1}}{x - 2}

\frac{\partial}{\partial x} (4 x e^{x})

\int_{0}^{\infty} x e^{- a x} d x

\frac{d}{d x} (\frac{e ^{2 x} - 1}{1 - e ^{- 2 x}})

\frac{d}{d x} ((x^{2} + 17) (x^{3} - 3 x + 1))

y^{^{''}} + 9 y = 9 x^{2} + 9 x + 11

What is the solution for (xdy)/(dx)-(2dy)/(dx)-(x-2)sin(x)+y=0 ?
The solution for (xdy)/(dx)-(2dy)/(dx)-(x-2)sin(x)+y=0 is y=-cos(x)+(sin(x))/(x-2)+(c_{1})/(x-2)