APMA 2101 Problem Set #3 Sample Solution Set(due 20 February 2007) Chapter 2: Review Problem Forx(y), we have dx/dy + x = y, with integrating factor exp(y). Integrating both sides and using integration by parts once on the right-hand side gives x(y)=c*exp(-y)+y-1. Section 2.4: Exact ODEs Section 6.1: The Euler Method 11. The exact solution, following the hint, is u(x) = tan(x+c), or with the initial condition and a return to the original variables, y(x)=tan(x+π/4)+1-x. Section 6.2: The Runge-Kutta Method
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