Using taylor's method, find ) y(0.1 correct to 3 decimal places from 2xy 1, y0 0 dx dy .
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Why would you want an approximate solution for this equation when you can have an exact one with very little trouble?
dy/dx = -2x(y^2). Separating variables, dy/(y^2) = -2xdx. Integrating both sides, -1/(2y) = -(x^2) + C. After some simple algebra, y = -1/[2(-(x^2) +C)]. Setting x = 0, y =-1/ 2C = 1 if C = -1/2.
I hope I did my algebra correctly. Of course, if this is a homework problem …
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