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Euler Method : Solve Analytically

I have a differential equation with the initial condition given by: dy/dx=y^2/x+1, where y(0)= 1 (see attached file for more detail).

As requested by my question, I have used the simple and improved euler methods to estimate y(1.2) with a step size of h=0.3 to 4 decimal places.

I am struggling to solve the differential equation analytically. Can you help?
I know that y(1.2) is 4.7272.


Solution Summary

The Euler method is used to solve a differential equation. The solution is detailed and well presented. The response received a rating of "5" from the student who posted the question.