Y'+y/x=sin x Помогите

[latex]y'+\frac{y}{x}=sinx\\\\y=uv\\\\u'v+uv'+\frac{uv}{x}=sinx\\\\u'v+u(v'+\frac{v}{x})=sinx\\\\1)v'+\frac{v}{x}=0\\\\\frac{dv}{dx}=-\frac{v}{x}\\\\\int \frac{dv}{v}=-\int \frac{dx}{x}\\\\ln|v|=-ln|x|\\\\v=x^{-1}=\frac{1}{x}[/latex] [latex]2)\; \; u'v=sinx\\\\\frac{du}{dx}=\frac{sinx}{v}=\frac{sinx}{\frac{1}{x}}=xsinx\\\\\int du=\int x\, sinx\cdot dx\\\\\int x\, sinx\cdot dx=[u=x,\, du=dx,\; dv=sinx\, dx,\; v=-cosx]=\\\\=-x\, cosx-\int (-cosx)dx=-x\, cosx+sinx+C\\\\3)\; \; y=uv=\frac{1}{x}(-xcosx+sinx+C)=-cosx+\frac{sinx}{x}+Cx[/latex]