Consider the following ODE: dy 2xy dx y² sin(x) + x² cos(y) With y(20) = 1.6 for 20 ≤ x ≤ 70. A. Use ode45() to solve the ODE and plot y against x with a resolution of 0.001. B. Use the midpoint method to solve the ODE with step sizes h = 0.01, 0.05, 0.1. Use a for loop to go through each value of h. Plot each of these on the same figure produced in part A. Remember to include a legend. Observe the differences in =

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Consider the following ODE:
dy
2xy
y² sin(x) + x² cos(y)
%3D
dx
With y(20)
1.6 for 20 < x < 70.
A. Use ode45() to solve the ODE and plot y against x with a resolution of 0.001. B. Use the midpoint method to solve the
ODE with step sizes h = 0.01, 0.05, 0.1. Use a for loop to go through each value of h. Plot each of these on the same figure
produced in part A. Remember to include a legend. Obselrve the differences in
Transcribed Image Text:Consider the following ODE: dy 2xy y² sin(x) + x² cos(y) %3D dx With y(20) 1.6 for 20 < x < 70. A. Use ode45() to solve the ODE and plot y against x with a resolution of 0.001. B. Use the midpoint method to solve the ODE with step sizes h = 0.01, 0.05, 0.1. Use a for loop to go through each value of h. Plot each of these on the same figure produced in part A. Remember to include a legend. Obselrve the differences in
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