ps3solutions - (1 Ah n =(1 At n/n n is exp(At n which shows...

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APMA 2101 Problem Set #3 Sample Solution Set (due 20 February 2007) Chapter 2: Review Problem For x(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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