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jaejoon89
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Homework Statement
F = (x^2 / y) i + y j + k
a) Use parametric equations to determine the equation for the flow line for the function F which passes thru the point (1,1,0)
b) Show that the flow line also passes thru the point (e,e,1)
Homework Equations
F = F1 i + F2 j + F3 k
dx/F1 = dy/F2 = dz/F3
The Attempt at a Solution
I didn't think parametric equations were actually needed here, but I think we're supposed to use them...
Somebody told me
x'[t] = x[t]2/y[t], y'[t] = y[t], z'[t] = 1 with the initial conditons that x[0] = 1, y[0] = 1, and z[0] = 0.
The solution is: x[t] = et, y[t] = et, z[t] = t
Setting t = 1 proves part b of the problem.
But I get
dx/(x^2 / y) = dt
dy/y = dt
dz = dt
Thus,
-y/x = t + c1 => x = -y / (t + c1)
ln|y| = t + c2 => y = c3e^t
z = t + c4
where c1, c2, c3, c4 are constants
What am I doing wrong? Also, why is t = 0?