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I've come cross the following first order nonlinear equation when trying to solve

for the speed of an electrical motor at any given timetduring motor start.

y'=-(ay^2)+bx+c;y(0)=0;a,bandcare 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.

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# 1st Order Nonlinear equation - Control

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