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- #1

\int_0^1yy'dx

\]

where \(y(0) = 0\) and \(y(1) = 0\).

The first integral is

\[

f - y'\frac{\partial f}{\partial y'} = c.

\]

Using this, I get \(yy' - y'y = 0 = c\) so ofcourse \(y(0)\) and \(y(1)\) equal \(0\) then but is this correct?

It just seems odd.