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( a ) Consider the modified problem d 2 y d t 2 + 2 y 2 d y d t + 4 y =
a Consider the modified problem
with
The ODE is very similar to except for the term in the lefthand side. Because of the
factor the ODE is nonlinear, while is linear. There is however very little to change
in the implementation of to solve In fact, the only thing that needs to be modified is
the ODE definition.
Modify the function defining the ODE in LABexm Call the revised file LABexm The
new function Mfile should reproduce the pictures in Fig
Include in your report the changes you made to LABexm to obtain LABexm
Figure : Time series and left and phase plot vs for
b Compare the output of Figs and Describe the changes in the behavior of the solution in
the short term.
c Compare the long term behavior of both problems and in particular the amplitude of
oscillations.
d Modify LABexm so that it solves using Euler's method with in the interval
use the file euler.m from LAB to implement Euler's method; do not delete the
lines that implement ode Let teYe be the output of euler, and note that Ye is a ma
trix with two columns from which the Euler's approximation to must be extracted. Plot
the approximation to the solution computed by odein black and the approximation
computed by euler in red in the same window you do not need to plot nor the phase
plot Are the solutions identical? Comment. What happens if we increase the value of
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