Bernoulli differential equation alike

Question

I am quite new to differential equations and I have the following $$ \partial u(x)/\partial x = a(x)u(x)^2+b(x)u(x)+c(x) $$ which is, to the best of my knowledge, not exactly a Bernoulli differential equation because of $c(x)$. Does anyone know which kind of equation is the one above and how to solve it? Thanks

Answer 1

This is a Riccati differential equation. There is no known way to solve it in general, but there are some strategies that work in many cases. You might look at this Maple help page.