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

  • Thread starter halycos
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I'm having issues approaching this problem. I need to solve for

Homework Statement



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

[itex]\frac{dy}{dt} + a \sqrt(y(t)) = b x(t)[/itex]

Homework Equations



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

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

[itex]\frac{1}{-a \sqrt(y(t)) + b x(t) } \frac{dy}{dt} =1 [/itex]

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

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