In Example 7 we saw that y(x) = 1/(C - x) defines a one-parameter family of solutions
Question:
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.
Example 7
Step by Step Answer:
Differential Equations And Linear Algebra
ISBN: 9780134497181
4th Edition
Authors: C. Edwards, David Penney, David Calvis