Euler's Method

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April 11th 2012, 03:11 PM
mathDad

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

Isn't $y_3 = y(.3)$ ?
April 11th 2012, 11:45 PM
a tutor

Re: Euler's Method

Your answer looks good.

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

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

You can probably get Wolframalpha to do this for you too.
April 12th 2012, 10:32 AM
mathDad

Re: Euler's Method

Quote:

Originally Posted by a tutor

Your answer looks good.

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

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

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

Thanks, tutor. Glad to have that confirmed (I always assume the book is right and tear out my hair looking for what I did wrong).
BTW, Wolframalpha is probably not allowed on the test we're studying for (just a hunch). But I guess I could have used it to confirm our answer.