# Nonlinear ODE - dy/dt=F(y(t),x(t))

1. Feb 17, 2013

### halycos

I'm having issues approaching this problem. I need to solve for

1. The problem statement, all variables and given/known data

Given the following equation, I need to find the max change in x(t) as y(t) changes, given bounds $y_{max}$ and $y_{min}$.

$\frac{dy}{dt} + a \sqrt(y(t)) = b x(t)$

2. Relevant equations

All ODE methods, MATLAB, or any method of solving, but not linearizing the equation

3. The attempt at a solution

I know an attempt would be nice, but I have looked at this for hours with no progress. I was thinking that it was close enough to use an integrating factor but I can't figure out how to handle integrating

$\frac{1}{-a \sqrt(y(t)) + b x(t) } \frac{dy}{dt} =1$

I found some ways to solve equations like this with systems of equations in matlab, but I know nothing else about this system Can anyone offer me any insight or a push in the right direction?

I can seemingly find that $h(0) = ( \frac{b}{a} x(0))^2$ (given that dh/dt at time 0 is 0), but I'm not sure how this would be useful.