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- Summary
- Are there real solutions to this ODE.

The ODE is:

\begin{equation}

(y'(x)^2 - z'(x)^2) + 2m^2( y(x)^2 - z(x)^2) = 0

\end{equation}

Where y(x) and z(x) are real unknown functions of x, m is a constant.

I believe there are complex solutions, as well as the trivial case z(x) = y(x) = 0 , but I cannot find any real solutions. Are there any, and if so how is best to find them?

Thanks for any help.

\begin{equation}

(y'(x)^2 - z'(x)^2) + 2m^2( y(x)^2 - z(x)^2) = 0

\end{equation}

Where y(x) and z(x) are real unknown functions of x, m is a constant.

I believe there are complex solutions, as well as the trivial case z(x) = y(x) = 0 , but I cannot find any real solutions. Are there any, and if so how is best to find them?

Thanks for any help.