st-order differential equation are shown in Figure 2.R.5.

Chapter , Problem 31RP

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Graphs of some members of a family of solutions for a first-order differential equation dy/dx = f(x, y) are shown in Figure 2.R.5. The graphs of two implicit solutions, one that passes through the point (1, -1) and one that passes through (-1, 3), are shown in blue. Reproduce the figure on a piece of paper. With colored pencils trace out the solution curves for the solutions \(y=y_{1}(x)\) and \(y=y_{2}(x)\) defined by the implicit solutions such that \(y_{1}(1)=-1\) and \(y_{2}(-1)=3\), respectively. Estimate the intervals on which the solutions \(y=y_{1}(x)\) and \(y=y_{2}(x)\) are defined

                                 

Text Transcription:

y = y_1 (x)

y = y_2 (x)

y_1 (1) = -1

y_2 (-1) = 3