Write the solution of the Cauchy p Þ(x) = x. Then write the solution with e any positive number. Show t 11

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12. Write the solution of the Cauchy problem with c= 1, 4(x) = cos(x) and
= x. Then write the solution with p(x) = cos(x)+e and ý(x) = x+e,
V(x) =
with e any positive number. Show that these solutions differ in magnitude
by no more than e(1 + T) for all x and 0 <t < T, for every positive
number T.
Transcribed Image Text:12. Write the solution of the Cauchy problem with c= 1, 4(x) = cos(x) and = x. Then write the solution with p(x) = cos(x)+e and ý(x) = x+e, V(x) = with e any positive number. Show that these solutions differ in magnitude by no more than e(1 + T) for all x and 0 <t < T, for every positive number T.
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