CHEN 3650 – HMWK 3.A
(due at the start of your next lab session)
For All Problems: clearly show your reasoning & methods
Throughout this course, you will be expected to solve differential equations of various types.
Below are several example equations with a boundary condition and a range for the
independent variable.
y’ = x y(0) = 1 x = 0..3 [1]
y’ = y y(0) = 1 x = 0..3 [2]
y’ = x4 y(0) = 1 x = 0..3 [3]
y’ = tan(x) y(0) = 1 x = 0..1 [4]
y’ = [cos(2y/x)]/[x+3] y(-1) = 1 x = -1..1 [5]
y’ = x cos(y) + y sin(x) y(0) = 1 x = 0..π [6]
Be aware that some of the above differential equations have no analytical solutions and/or are
not continuous over the specified range. Numerically solve all of the differential equations
using both the Euler method and the Runge-Kutta Fourth Order (RK4) method. Use each of
the following step sizes: 1% & 0.1%. Report the difference between your numerical solution
(Euler & RK4) and the exact solution at the endpoint of the specified range for each
equation. In any cases where no analytical solutions exist, report the difference with respect
to the RK4 estimate using the smallest step size. In the event that the specified step size does
not exactly reach the endpoint of the range, stop one specified step below the endpoint and
use one final step of selectable size to finish integration at exactly the endpoint.
