I've got the IVP:
(1-x^2)y'-xy=1 subject to y(0)=0
I can solve this to obtain: y= arcsinx/(1-x^2)^(1/2)
Then we're told to use Euler's method but in the solutions the ODE is written so that u(t)=y(x) and then we have y′ = f(x, y) = sinx−y, y(0) = 1
How come this happens? And how do you obtain that?
But we haven't even met!