Hi, All: I am taking a course of quantitative trading given by a Wall street trader, and have be given some maths questions. But two of them I cannot do.Question 1: solve the ODE: dy/dx = x+ x^2*y + x^3*y^2Question 2: for a control system that has the dynamic of dx/dt = u(t)with |u(t)|<=1 for all t in [0,T], with terminal condition V(T,x) = 1/2 x^2;1. what is the (most obvious) optimal control policy (without doing any mathematics )?2. What is the cost function J*(t,x);3. What is the HJB equation?4. Can you solve for the HJB equation?

For the question 1, I have checked with Mapple and Mathematica and I fear that you won't find the solution easily (it involves a very rare and exotic kind of special function). Try with a serie expansion maybe.

I think that's a Riccati equation: y'(x) = q0(x) + q1(x)*y + q2(x)*y^2In the Wikipedia you can find a method to solve the equation. RiccatiEqHope it helps.

another duplicate post

You may have a look also hereRiccati equation on eqworld You will have to transform into a second order linear ODE and then probably solve it with series. It will be transformed into the linear ODE u''-3x*u'+x^4*u=0 if I'm right.