This table compares the results of numerical calculations, using Euler and second order Runge-Kutta to solve

y¢ = 1-2xy ;       y(0) = 0

The analytic result is also included.

xn 0.0 0.1 0.2 0.3 0.4 0.5

yn Euler 0.00000 0.10000 0.19800 0.29008 0.37268 0.44287

yn 2nd order Runge-Kutta 0.000000 0.099500 0.195045 0.282988 0.360273 0.424645

y(xn) Analytic 0.00000 0.09934 0.19475 0.28263 0.35994 0.42444