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## Homework Statement

Solve the System of DEs:

[itex]\sqrt{1+y'^{2}+z'^{2}}-\frac{y'^{2}}{\sqrt{1+y'^{2}+z'^{2}}}=C_{1}[/itex]

[itex]\sqrt{1+y'^{2}+z'^{2}}-\frac{z'^{2}}{\sqrt{1+y'^{2}+z'^{2}}}=C_{2}[/itex]

## Homework Equations

The two equations above are quite relevant.

## The Attempt at a Solution

I attempted basic substitution to do is this:

Multiply through by the radical

Cancel terms

Solve for y' and z' in terms of each other

Plug them into each other and then attempt to solve

I ended up trying to solve for y' first. What I got is a solvable polynomial in terms of y'; a quite tedious looking polynomial at that. I stopped here and began erasing. Maybe I was doing it right, but I don't even want to see what happens when I plug it into the quadratic equation and then attempt to substitute it back into the z' equation.. It sounds like WAYYY to long of a process considering this is physics homework, not math homework.

Can anybody give me some advice? Any good way to approach problems like these? I'm starting to encounter them a lot and it's always the part of the problem that I spend hours looking at :\