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I've got a one-dimensional non-autonomous ODE of the following form:

dy / dx = f(x,y;w)

x_{0} = g(w)

y_{0} = h(x_{0};w)

--- i.e., w is a parameter that influences both the derivative dy/dx along with both coordinates in the initial condition (x_{0},y_{0}). I basically want to learn if an increase in w will raise or lower y at some given x.

Can anyone recommend a good reading? I studied qualitative ODEs a while ago, but it was mainly about the stability and long-run behaviour of solutions and always in the context of autonomous systems.

Thanks very much!

Best,

T

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# Qualitative implications of parameter shift in non-autonomous ODE

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