Thank you for the fast answer!
I solved the ODE already for specific coefficients, also I can draw a phase diagramm. Only the direction field is missing.... I thought recently that this direction field has to go out from the invariant equation; but that seems wrong.
Mathcad 15 is installed, but I dont like the input of some way...so I am using Prime 2 mainly with a license from my university.
The sheet named "VectorField_P2" seems promising. I just realized that this is from you. So thanks for that! Playing around with this sheet and I think I am on to something.