DSolve return undesired value?

Questions
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1

Hi,

I’m using DSolve to optimize via Euler-Lagrange with an integral constraint some problem. Nevertheless, the output of DSolve returns values and not functions, and some of these values are undesired (impossible from physics). For instance, some optimal value result in “a=-1”, but this parameter just has sense higher than zero. How can I restrain these solution space? The example is attach in the notebook, where l am is the Lagrange multiplier.

Thank you so much.

ExForum.nb (7.81 KB)

2

What is the meaning of D[F, a'[x]]? Mathematica returns 0. Your differential equation turns up not to involve derivatives.

3

is the derivative of the function respect to the da/dx, as the Euler Lagrange requires. But there is no derivative in the function, then it turns to zero.