1. ## Euler's Method

From an AP Calculus BC exam guide book:
Use Euler's method with step increment h=0.1 to approximate y(0.3), where y(x) is the solution to the IVP y'=y+xy, y(0)=1.

We think the answer is (C) 1.37. The answer key says the answer is (E) 1.54. I think the book gave the answer for y(0.4). Are we right? Is the book?

PS. Answers A,B, and D are: 1.221, 0.1, and 1.1.

​Edit: OK, some more detail:
$\displaystyle y_0=1,\ x_0=0$
$\displaystyle m=y'(0,1)=1+0 \cdot 1=1$
$\displaystyle y_1=y_0+h \cdot m=1+.1 \cdot 1= 1.1$
$\displaystyle m=y'(0.1,1.1)=1.1+0.1 \cdot 1.1=1.21$
$\displaystyle y_2=y_1+h \cdot m=1.1+.1 \cdot 1.21= 1.221$
$\displaystyle m=y'(0.2,1.221)=1.221+0.2 \cdot 1.221=1.4652$
$\displaystyle y_3=y_2+h \cdot m=1.221+.1 \cdot 1.221= 1.36752 \approx 1.37$

Isn't $\displaystyle y_3 = y(.3)$?

2. ## Re: Euler's Method

By the way, this one is easy to solve exactly.

You get $\displaystyle y=e^{x^2/2+x}$ so $\displaystyle y(0.3)\approx 1.412$.

You can probably get Wolframalpha to do this for you too.

3. ## Re: Euler's Method

Originally Posted by a tutor
You get $\displaystyle y=e^{x^2/2+x}$ so $\displaystyle y(0.3)\approx 1.412$.