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Notes on Diffy Qs - Sage demos for section 1.3

Press the Evaluate button below to launch the Sage demonstration. You may have to wait a little before the graph appears. Be patient. To change the function, you should edit the code and press the Evaluate button again.

Plotting implicit solutions

Here we show how one uses Sage to plot implicit solutions, that is, we plot some equation in \(x\) and \(y,\) where we do not know how to simply solve for \(y.\) Note that in the Sage code when giving equality for the equations we use "==" rather than just one "=". By default, we are plotting \(y^2+2\ln|y|=x^2 , \) which was the one we found in the book in Example 1.3.2. Note that the solution \(y(x)\) satisfying the initial condition \(y(1)=0\) is just the top curve.

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