Question Sheet 9 - Challenge Problem

1. a) Solve the 1st order ODE (dy/dx)=a*cos(ax), with y(0)=0.

b) Define a function with the solution of the DE.

c) Define a function which plots the solution of the DE for a number of different values of a.

d) Test if your function works for a specific value of a.

e) Plot a manipulate with a varying from 1 to 5.

2. a) define a function for sin(ax)*cos(bx).

b) Define a function that plots the above function over the range 0 to 4π for both x and y. What is more appropriate to use ‘:=’ or ‘=’?

c) Use manipulate to plot sin(ax)*cos(bx), with a and b varying over the range 0.1 to 2.