Find the integral curves of the following vector field: $\displaystyle V=(\log(y+z),1,-1)$.
I don't even know how to start.....
By definition of integral curve, you have to find the family of curves:
$\displaystyle \gamma (t)=(x(t),y(t),z(t))$
such that
$\displaystyle \gamma'(t)=V(\gamma (t))$ .
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Solve the system:
$\displaystyle \begin{Bmatrix}x'=\log (y+z)\\y'=1\\z'=-1\end{matrix} $
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