In Example 7 we saw that y(x) = 1/(C - x) defines a one-parameter family of solutions

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In Example 7 we saw that y(x) = 1/(C - x) defines a one-parameter family of solutions of the differential equation dy/dx = y2.


(a) Determine a value of C so that y (10) = 10.


(b) Is there a value of C such that y(0) = 0? Can you nevertheless find by inspection a solution of dy/dx = y2 such that y(0) = 0?


(c) Figure 1.1.8 shows typical graphs of solutions of the form y(x) = 1/(C - x). Does it appear that these solution curves fill the entire xy- plane? Can you conclude that, given any point (a, b) in the plane, the differential equation dy/dx = y2 has exactly one solution y(x) satisfying the condition y(a) = b?


FIGURE 1.1.8. Graphs of solutions of the equation dy/dx = y2.


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Example 7


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Differential Equations And Linear Algebra

ISBN: 9780134497181

4th Edition

Authors: C. Edwards, David Penney, David Calvis

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