Qualitative analysis is the first step in solving first-order ode. Qualitative analysis can be used to verify numerical and analytic solutions. Even if an explicit formula is known, qualitative analysis is useful, since it can give a visual picture of the behavior of solutions to an ode. We consider autonomous and non-autonomous ode separately.
Remember an autonomous first-order ode has the form y'=f(y). The derivative is a function of the dependent variable only. Here is an example:
Click here to learn about qualitative analysis of autonomous ode.
A non-autonomous first-order ode has the more general form y=f(t,y). The derivative is a function of both the dependent and independent variables. Here is an example:
Click here to lean about qualitative analysis of more general non-autonomous ode.
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