OpenStudy (anonymous):

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.

2 years ago
zepdrix (zepdrix):

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

2 years ago
OpenStudy (anonymous):

Hi, thanks! Yeah that would have been bad

2 years ago
OpenStudy (anonymous):

can u help me

2 years ago
OpenStudy (anonymous):

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

2 years ago
zepdrix (zepdrix):

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

2 years ago
zepdrix (zepdrix):

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:\[\Large\rm y_{n+1}=y_1+h\cdot f(y_n,x_n)\]

2 years ago
zepdrix (zepdrix):

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

2 years ago
OpenStudy (anonymous):

my post does'nt work that why

2 years ago
zepdrix (zepdrix):

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

2 years ago
OpenStudy (anonymous):

yes

2 years ago
zepdrix (zepdrix):

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:\[\Large\rm y_2=y_1+\frac{1}{10}f(y_1,x_1)\]

2 years ago
zepdrix (zepdrix):

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

2 years ago
zepdrix (zepdrix):

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

2 years ago
zepdrix (zepdrix):

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

2 years ago
OpenStudy (anonymous):

Yeah i do not understand

2 years ago