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2. (Classification of Equations)
f(x, j) is defined
to he separable provided functions F and G exist
the prohleiiis that can
be converted into separable form. No details ex—
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2
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f(x, y) which is not separable, not quadrature, but it is linear.
(c) [20%] Apply a classification test to show that p’ +tan(z)g = —1 —x+iry is a linear differential
equation. Supply all details, including a statement of the test.
(d) [30%] Apply a classification test to show that p’
details, including a statement of the test.
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‘K 9
Nanie.
5. (Stability)
(a) [50%] Draw a phase line diagram for the dliffereiltial equation
eta;
(3—t2a:—
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2
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4)(a
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(z
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(b) [50%] Assume an autonomous equation z’(t) = f(a(t)). Draw a phase diagram with
at least
12 threaded curves, using the phase line diagram given below. Add these labels
as appropriate:
funnel, spout, node [neither spout nor funnel], stable, unstable.
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