- #1
madachi
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Homework Statement
Find the flow line curve [itex] c(t) [/itex] to the vector field [itex] F = (x,-y) [/itex] which passes through the point [itex] (1, 2) [/itex].
The Attempt at a Solution
So I let [itex] c(t) = (x(t), y(t)) [/itex].
So [itex] c'(t) = ( \frac{dx}{dt} , \frac{dy}{dt} ) [/itex].
Now, [itex] \frac{dx}{dt} = x [/itex] and [itex] \frac{dy}{dt} = -y [/itex].
So [itex] \frac{dy}{dx} = -\frac{y}{x} [/itex]
Solving the differential equation, I get
[itex] ln(y) = -ln(x) + C [/itex]
[itex] y = e^{-ln(x) + C} [/itex]
[itex] y = \frac{A}{x}[/itex]
[itex] y = \frac{2}{x} [/itex] by using the point given.
This is not the answer given, I am not sure what they want. The answer given is
[itex] c(t) = ( e^{t}, 2e^{-t} ) [/itex].
Thanks.
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