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That ODE took me a little while to solve... I had to switch from dy/dx to dx/dy, do a Bernoulli substitution, two applications of integration by parts, and then some algebraic manipulations in order to solve it.

The final result?

y = (x^3-4)/12

This really simple equation which satisfies the ODE leads me to believe that there is an easier method for solving this... A few of these might appear on my final tomorrow, and I don't want to spend all of that time if there is an easier method.

Thanks!