Set of ODEs with an additional condition

Hello, Let's say we have the following system of equations: x'=x+sin(y) y'=y+x And we know the boundary conditions. Also, we have the following condition that must be met in the solution of the two equations: log(x)+exp(x)-2*sin(y^2)=0 Is there an official title for this kind of problems? How to solve this system? Thank you!

Answer 1

[J. Alex Lee]

I think this is a differential algebraic equation (DAE)?

Documentation for ode15s might help.

Answer 2

[Torsten]

The two differential equations uniquely determine x and y. So you can't expect the algebraic relationship

log(x)+exp(x)-2*sin(y^2)=0

to be satisfied for the solution of the two differential equations

x'=x+sin(y) , y'=y+x.

Best wishes

Torsten.