Integral Curves

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January 26th 2011, 10:51 AM
mathematicalbagpiper

Integral Curves

Find the integral curves of the following vector field: $V=(\log(y+z),1,-1)$ .

I don't even know how to start.....
January 26th 2011, 11:12 AM
FernandoRevilla

Quote:

Originally Posted by mathematicalbagpiper

I don't even know how to start.....

By definition of integral curve, you have to find the family of curves:

$\gamma (t)=(x(t),y(t),z(t))$

such that

$\gamma'(t)=V(\gamma (t))$ .

Fernando Revilla
January 26th 2011, 11:40 AM
mathematicalbagpiper

And to do that you do what?
January 26th 2011, 12:10 PM
FernandoRevilla

Quote:

Originally Posted by mathematicalbagpiper

And to do that you do what?

Solve the system:

$\begin{Bmatrix}x'=\log (y+z)\\y'=1\\z'=-1\end{matrix}$

Fernando Revilla

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