A basic theorem states that a linear differential equation of order n has a general

Chapter 9, Problem 67

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A basic theorem states that a linear differential equation of order n has a general solution that depends on n arbitrary constants. The following examples show that, in general, the theorem does not hold for nonlinear differential equations. (a) Show that (y )2 + y2 = 0 is a first-order equation with only one solution y = 0. (b) Show that (y )2 + y2 + 1 = 0 is a first-order equation with no solutions. 6

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