I'm trying to solve a two point boundary value problem with a piecewise system of equations like:

dx[t_] := Piecewise[{{0, y[t] &lt;= 0}, {x[t]^(3/4) - x[t], y[t] &gt; 0}}]
dy[t_] := Piecewise[{{0, y[t] &lt;= 0}, {(1 - y[t])/x[t]^(1/4) + y[t], y[t] &gt; 0}}]

NDSolve[{x'[t] == dx[t], y'[t] == dy[t], x[0] == 1, y[10] == 2}, {x, y}, {t, 0, 10}]


which produces the error

 NDSolve::bvdisc: NDSolve is not currently able to solve boundary value problems with discrete variables.


I tried the answers here by entering

funs = ParametricNDSolveValue[{x'[t] == dx[t], y'[t] == dy[t], x[0] == 1, y[10] == yt}, {x, y}, {t, 0, end}, yt]

FindRoot[funs[yt][end], {yt, 2}]


which yields the same error.

Is there any way to solve this system? Thanks for the help.


Question: Fuzzy Logic in Finance
Answer: Actually it has - in combination with Neural Nets. The NN is used to evaluate the fitness of fuzzy trading rules. A company that does these kinds of things is Siemens (esp. their research department 'Corporate Technology'). Siemens uses NNs quite successfully for their own trading/hedging commodities (e.g. copper, electricity)

Supplement: As a starting point please have a look at:
Siekmann, S.; Neuneier, R.; Zimmermann, H.G.; Kruse R.: Neuro Fuzzy Systems for Data Analysis, In: Computing with Words in Information / Intelligent Syst. 2; Eds.: Zadeh L. A., Kacprzyk J.;p. 35-74; Physica Verlag; 1999

Especially one of the authors, Dr. Hans-Georg Zimmermann is one of the most renowned experts in Neural Networks and Neural mathematics.