Assignment:
The function of y(x) satisfies the differential equation dy/dx = x2 + 1/ y and the initial
condition y(1)=1. Firstly solve the equation to get an exact value then Use Eulers method to obtain the value of y(2). Compare this value with the analytical value and discuss how the approximate value obtained by Euler’s method may be improved.
Provide complete and step by step solution for the question and show calculations and use formulas.