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

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

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- Jan 26th 2011, 10:51 AMmathematicalbagpiperIntegral Curves
Find the integral curves of the following vector field: $\displaystyle V=(\log(y+z),1,-1)$.

I don't even know how to start..... - Jan 26th 2011, 11:12 AMFernandoRevilla
By definition of integral curve, you have to find the family of curves:

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

such that

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

Fernando Revilla - Jan 26th 2011, 11:40 AMmathematicalbagpiper
And to do that you do what?

- Jan 26th 2011, 12:10 PMFernandoRevilla

Solve the system:

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

Fernando Revilla