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anonymous
 4 years ago
5. Consider the differential equation
dy/dt= y − t.
(a) Work out by hand three steps of Euler’s method with step size .25 for the above
equation, with y(1) = 1.
anonymous
 4 years ago
5. Consider the differential equation dy/dt= y − t. (a) Work out by hand three steps of Euler’s method with step size .25 for the above equation, with y(1) = 1.

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Euler’s method is a method that's used to approximate solutions of initial value problems of the form \(y'=f(t,y), y(t_0)=y_0\). In each iteration you should apply \(y_{n+1}=y_n+hf(t_n,y_n)\), where h is the step size. I will help you with the first iteration on the next post.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Before I start, you need to notice that \(f(t,y)=yt\). Iteration#1 (\(n=0)\): In this iteration we have \(y_n=y_0=1, t_n=t_0=1, \) and \(f(t_n,y_n)=f(t_0,y_0)=0.\) Hence \(y_1=y_0+hf(t_0,y_0)=1+0.25(0)=1\)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0You might want to watch this video here http://www.youtube.com/watch?v=4CqaepeaJHA
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