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1. We discussed at length the "shooting method" for solving differential equations. Use it to solve the simple differential equation y" = y, = = = 5.81. You will need to subject to the boundary conditions (BCs) y(0) 3 and y(1) guess an initial slope y'(0). A suitable tolerance for knowing when you are close enough to the BC at x = 1 to quit is up to you but there is no need to be too stringent. Perhaps try a tolerance tol 103. The choice is up to you. By solution, I mean your code should print your final estimate of the initial slope y'(0), your computed value of y(1) to show how close you came, and a plot showing y(x) over the x-interval [0,1]. As further guidance, I recommend you insert simple code that adjusts the initial slope slightly for each iteration of calling solve ivp. An increment/decrement of ±0.1 or so may prove useful. This will save you some time guessing the initial slope.

1. We discussed at length the "shooting method" for solving differential equations. Use it to solve the simple differential equation y" = y, = = = 5.81. You will need to subject to the boundary conditions (BCs) y(0) 3 and y(1) guess an initial slope y'(0). A suitable tolerance for knowing when you are close enough to the BC at x = 1 to quit is up to you but there is no need to be too stringent. Perhaps try a tolerance tol 103. The choice is up to you. By solution, I mean your code should print your final estimate of the initial slope y'(0), your computed value of y(1) to show how close you came, and a plot showing y(x) over the x-interval [0,1]. As further guidance, I recommend you insert simple code that adjusts the initial slope slightly for each iteration of calling solve ivp. An increment/decrement of ±0.1 or so may prove useful. This will save you some time guessing the initial slope.

C++ for Engineers and Scientists
C++ for Engineers and Scientists
4th Edition
ISBN:9781133187844
Author:Bronson, Gary J.
Publisher:Bronson, Gary J.
Chapter5: Repetition Statements
Section5.7: Do While Loops
Problem 6E: (Numerical analysis) Here’s a challenging problem for those who know a little calculus. The...
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please write the code for this problem using python in a jupyter notebook. I am stuck

1. We discussed at length the "shooting method" for solving differential equations. Use it to solve the simple differential equation y" = y, = = = 5.81. You will need to subject to the boundary conditions (BCs) y(0) 3 and y(1) guess an initial slope y'(0). A suitable tolerance for knowing when you are close enough to the BC at x = 1 to quit is up to you but there is no need to be too stringent. Perhaps try a tolerance tol 103. The choice is up to you. By solution, I mean your code should print your final estimate of the initial slope y'(0), your computed value of y(1) to show how close you came, and a plot showing y(x) over the x-interval [0,1]. As further guidance, I recommend you insert simple code that adjusts the initial slope slightly for each iteration of calling solve ivp. An increment/decrement of ±0.1 or so may prove useful. This will save you some time guessing the initial slope.
Transcribed Image Text:1. We discussed at length the "shooting method" for solving differential equations. Use it to solve the simple differential equation y" = y, = = = 5.81. You will need to subject to the boundary conditions (BCs) y(0) 3 and y(1) guess an initial slope y'(0). A suitable tolerance for knowing when you are close enough to the BC at x = 1 to quit is up to you but there is no need to be too stringent. Perhaps try a tolerance tol 103. The choice is up to you. By solution, I mean your code should print your final estimate of the initial slope y'(0), your computed value of y(1) to show how close you came, and a plot showing y(x) over the x-interval [0,1]. As further guidance, I recommend you insert simple code that adjusts the initial slope slightly for each iteration of calling solve ivp. An increment/decrement of ±0.1 or so may prove useful. This will save you some time guessing the initial slope.
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