(a) Show that y.x/ D Cx4 denes a one-parameter family of differentiable solutions of the
Chapter 3, Problem 48(choose chapter or problem)
(a) Show that y.x/ D Cx4 denes a one-parameter family of differentiable solutions of the differential equation xy0 D 4y (Fig. 1.1.9). (b) Show that y.x/D(!x4 if x<0 , x4 if x = 0 denesadifferentiablesolutionofxy0D4y forallx, butis not of the form y.x/DCx4. (c) Given any two real numbers a and b, explain whyin contrast to the situation in part (c) of exist innitely many differentiable solutions of xy0D4y that all satisfy the condition y.a/D b.
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