I would like to understand my calc homework:/
posted by Amber .
Consider the differential equation given by dy/dx=(xy)/(2)
A) sketch a slope field (I already did this)
B) let f be the function that satisfies the given fifferential equation for the tangent line to the curve y=f(x) through the point (1,1). Then use your tangent line equation to estimate the value of f(1.2).
C) find the particular solution y=f(x) to the differential equation with the initial condition f(1)=1. Use your solution to find f(1.2).
D) compare your estimate of f(1.2) found in part b to the actual value of f(1.2)
E) was the estimate under or over? Use the slope field to explain why?
You need to have patience and not post the same stuff umpteen times. The tutors who concentrate on this type of math are not online yet.
Please do not keep posting the same question over and over. It's considered spamming and could get you banned from posting here.
at (1 , 1) dy/dx = slope = 1*1/2 = .5
y = .5 x + b is tangent for some b
put in (1 , 1 )
1 = .5 + b
b = .5
so tangent at (1,1) is
y = .5 x + .5
at x = 1.2
y = .5(1.2) + .5 = 1.1
dy/y = (1/2) x dx
ln y = (1/4) x^2 + C
y = k e^(x^2/4)
1 = k e^(1/4)
1 = 1.28 k
k = .779
y = .779 e^(x^2/4)
at x = 1.2
y = .779 e^(1.44/4)
y = .779 * 1.433
y = 1.116
Do not panic. Plug and chug.
I think the whole non panicing ship sailed a long time ago haha. Sorry and thanks for the help!