Exercise

1. Find the direction field and solution curve through the points $(1,0),(0,1),(1,1)$.
$(a) \ y^{\prime} = y$
$(b) \ y^{\prime} -xy + 1 = 0$
2. Find the approximated solution of the following initial value problem by using Euler's method.
(a) For $y^{\prime} = x + y, \ y(0) = 0$, find $y(3)$ provided $h=1$
(b) For $y^{\prime} = x^{2}, \ y(1) = 2$, find $y(4)$ provided $h = \frac{1}{2}$