Here’s a short question that will give you an opportunity to practice using Euler’s Method. Complete this before our lesson tomorrow.
Use Euler’s Method to find the approximate value of \(f(3)\) if \(y=f(x)\) is the solution to
\[\frac{\textrm{d}y}{\textrm{d}x} = y^2-x\]passing through \((2,1)\). Use a step length of \(0.5\).
(Notice that this is a first-order nonlinear DE that is neither separable hor homogeneous, so we won’t be able to use any methods available in the course to find an explicit solution for this DE.)