What are all solutions to the differential equation
$$ u'(x)v(x) + u(x)v'(x) = u'(x)v'(x) $$
Where the derivative is with respect to $x$.
What are all solutions to the differential equation
$$ u'(x)v(x) + u(x)v'(x) = u'(x)v'(x) $$
Where the derivative is with respect to $x$.