Maybe I am getting my ODE's and PDE's mixed up

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Originally Posted by

**Richyie** in not sure what you mean by a direction field ?

say we had a quasilinear pde a*du/dx+b*du/dy = c . Lecture notes say: charactaristics satisfy dx/a = dy/b = du/c

from the above we can deduct integrals I, J such that I=constant and J = constant.. fair enough

and when these integrals intersect we get a charactaristic curve.. . ..

or am i understanding this incorrectly, just trying to picture it, its confusing(Crying) what does it look like geometrically ? ?

but if you assigned the two derivatives a value c and d...then you assign them numbers and graphed them you would get a three dimensional graph which shows the slope at each point