$h=0.15, y(0.6)=?, y'=x(y+x)-2,y(0)=2$ , anwer correct upto 5 decimal places using Euler method

Question

use euler's method with step size $h=0.15$ to compute the approximate value of $y(0.6)$,correct upto five decimal places from initial value problem

$$y'=x(y+x)-2,\, \, y(0)= 2$$

Actually, I have found the answer for $y(0.6)$ with $h=0.15$ but i doesn't know wether the answer is correct upto 5 decimal places or not. How can i check the error and get the answer correct upto 5 decimal places?

Answer 1

If they give you a method and a step size they shouldn't ask you to maintain a certain accuracy. It would make more sense to ask you to choose the step size to get the accuracy desired. You could solve the differential equation to get the exact answer and check yours against it, or you could use the derivatives of the solution in the error formula for the method to get a step size.