Question

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?

Answer 1

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.

Answer 2

Please do not keep posting the same question over and over. It's considered spamming and could get you banned from posting here.

Answer 3

B)
at (1 , 1) dy/dx = slope = 1*1/2 = .5
so
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
==========================
C)
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
etc

Answer 4

Do not panic. Plug and chug.

Answer 5

I think the whole non panicing ship sailed a long time ago haha. Sorry and thanks for the help!