From an AP Calculus BC exam guide book:

Use Euler's method with step incrementh=0.1to approximatey(0.3), wherey(x)is the solution to the IVPy'=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 fory(0.4). Are we right? Is the book?

PS. Answers A,B, and D are:1.221,0.1, and1.1.

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 $\displaystyle y_3 = y(.3)$?