y'+x*(y^1/3)=3y

y'-3y=-x*(y^1/3)
y=uv, y'=u'v+v'u
u'v+v'u-3uv=-x*(uv)^(1/3)
u'v+u(v'-3v)=-x*(uv)^(1/3)
(v'-3v)=0, v=e^(3x)

u' e^(3x) =-x*(u)^(1/3)* e^(x)

du/(u)^(1/3) = -xe^(-2x) dx

3/2*(u^2/3)=e^(-2x)*(2x+1)/4+C1

u^(2/3)=e^(-2x)*(2x+1)/6+C
u=[e^(-2x)*(2x+1)/6+C]^(3/2)

y=u*v=[e^(-2x)*(2x+1)/6+C]^(3/2)*e^(3x)