Use Euler's method with step size 0.1 to estimate y(1.5), where y(x) is the solution of the initial-value problem y' = 3y + 2xy, y(1) = 1.

Question

zepdrix · Answer

Hey Sarah :) Welcome to OpenStudy!

Oh boy I thought we were starting from x=0, 15 steps, that woulda been brutal lol

anonymous · Answer

Hi, thanks! Yeah that would have been bad

anonymous · Answer

can u help me

anonymous · Answer

Select all sets that contain the number 1/2.
	A.	Integer
	B.	Irrational
	C.	Natural
	D.	Rational
	E.	Whole

Select all that apply

zepdrix · Answer

Baby ask a new question on the left side :) Don't interrupt someone else's question silly!

zepdrix · Answer

So we have our derivative function in terms of the other two variables,$$\Large\rm y'=f(x,y)$$

Euler tells us an iterative method for approximating the solution:$$\Large\rm y_{n+1}=y_1+h\cdot f(y_n,x_n)$$

zepdrix · Answer

Hmm let's see if we can figure this out..

anonymous · Answer

my post does'nt work that why

zepdrix · Answer

So our starting point is $\Large\rm y(1)=y_1=1$

anonymous · Answer

yes

zepdrix · Answer

Ok so we're letting our step size be a tenth, that works out nicely.
So we'll take 5 steps then, counting by 1's.

So our first approximation will be:$$\Large\rm y_2=y_1+\frac{1}{10}f(y_1,x_1)$$

zepdrix · Answer

$$\Large\rm f(y_1,x_1)=y'(y_1,x_1)=y'(1,1)=3(1)+2(1)(1)$$

zepdrix · Answer

Do you understand how I figured out that derivative value? :o

zepdrix · Answer

Too much crazy math stuff?
Did you brain esplode already? :( uh oh

anonymous · Answer

Yeah i do not understand