Use euler's method with step size 0.2 to estimate y(1), where y(x) is the solution of the initial-value problem

Question

y'= -3x+y^2, y(0)=1

Answer 1

what's the problem? Just plug and chug:

Y_i+1 = y_i + .2*y'(x_i,y_i)

0: (0.0000,1.0000) -> 1.2000
1: (0.2000,1.2000) -> 1.3680
2: (0.4000,1.3680) -> 1.5023
3: (0.6000,1.5023) -> 1.5937
4: (0.8000,1.5937) -> 1.6216
5: (1.0000,1.6216) -> 1.5475

Looks like f(1) = 1.6216