So I've never taken differential equations, but this problem popped up in an Econ class so I'm pretty lost.

Let R(w) = {(-w)[u''(w)]}/u'(w)

Suppose R(w) = r > 0 for all w.

Derive an expression for u(w).

So i began by multiplying both sides by u'(w) and then bringing everything over to the left. I'm not sure where to introduce d/dw. I guess I'm pretty lost. There was a hint: let z(w) = u'(w) and solve the differential equation for z.

This then becomes:

R(w) = {(-w)[z'(w)]}/z(w)

[z(w)]R(w) = -w[z'(w)]

[z(w)]R(w) + w[z'(w)] = 0

Then I'm stuck.

Thanks in advance for the help.