(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

integrate dy/dx = (1+e^y)(1+x) from x=0 using the improved euler method taking step sizes of 0.125. compare the numerical solution of y(0.5) with the exact value

3. The attempt at a solution

Firstly to find the exact value I use seperation of variables and the initial condition y(0)=0 to find that y=-ln[-1+2e^(-x)e^{-(x^2)/2}]

Subbing in x=0.5 yields 2.6518

However, using an advanced euler calculator i found online tells me this:

x_n y_n

0.00000 0.00000

0.12500 0.28560

0.25000 0.67185

0.37500 1.25597

0.50000 2.45219

That is, y(0.5)=2.45219

I was just wondering if somebody would be able to confirm this is correct.

Thanks!

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# Homework Help: Advanced euler method query

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