Question

y'+y/x=3 Помогите решить

Answer 1

$y'+ frac{y}{x} =3 \ y=uv \ y'=u'v+uv' \ u'v+uv' +frac{uv}{x}=3 \ v(u'+frac{u}{ x})+uv'=3 \ left { {{u'+frac{u}{x}=0} atop {uv'=3}} right. \ u'+frac{u}{x}=0 \ u'=-frac{u}{x} \ frac{du}{u} =-frac{dx}{x} \lnu=-lnx \ u= frac{1}{x} \ frac{v'}{x}=3 \ dv}=3xdx \ v= frac{3x^2}{2} +C \ y=frac{1}{x}(frac{3x^2}{2} +C )$