Answer:
1.5
Step-by-step explanation:
The Euler's method is a common approximation method for the solution of differential equations. It can be used to obtain an approximate value of a given function. The Euler's formula is:
[tex]y_{n} = y_{n-1} + hF(_{x_{n-1},y_{n-1}})[/tex]
Therefore, n =1 will give:
[tex]y_{1} = y_{0} + hF(x_{0},y_{0})[/tex]
h is the step size and it is equivalent to [tex]\frac{x_{1}-x_{2}}{2} = \frac{1-0}{2}=\frac{1}{2}[/tex]
[tex]F(x_{0},y_{0}) = x_{0} + y_{0} = 0 + 1 = 1[/tex]
[tex]y_{1} = 1 + (0.5)(0+1) = 1 + (0.5)(1) = 1 + 0.5 = 1.5[/tex]
