1st Order Nonlinear equation - Control

[danielgdls]

Hello everybody,


I've come cross the following first order nonlinear equation when trying to solve
for the speed of an electrical motor at any given time t during motor start.

y'=-(ay^2)+bx+c ; y(0)=0 ; a, b and c are constants; y=motor speed; x= time

The Motor Starter uses a linear Torque control and the load exhibits a quadratic
dependence of the motor speed. I am sure there is a possibility of solving this analitically.
I've tried changing variables, reduction and using substitution with no success. Maybe I
am missing something or haven't found the right substitution...Any ideas? I'll appreciate
any help on this.

Daniel.

 

[quantumdude]

I plugged it into Maple, and there is indeed a closed form solution. But it's a complicated mess of Airy functions, so I don't think there's a "silver bullet" substitution that's going to make this nice for you.