The direction fields of three DEs are shown in Fig. 2.2.3. (a) Label the equations linear or
Question:
(a) Label the equations linear or nonlinear. Of the two that are linear, which is homogeneous and which is non homogeneous?
(b) Explain (algebraically) why the sum of two solutions of a homogeneous linear DE is a solution. Verify that the negative of such a solution is also a solution, so y = 0 must be a-solution.
(c) Interpret the observations of pan (b) for the direction fields in Fig. 2.2.3. Visualize two solutions and then their sum. Does the sum follow the direction field?
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a A is linear homogeneous B is linear non homogeneous C is nonlinear b If y 1 and y 2 are solutions ...View the full answer
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Related Book For 
Differential Equations and Linear Algebra
ISBN: 978-0131860612
2nd edition
Authors: Jerry Farlow, James E. Hall, Jean Marie McDill, Beverly H. West
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