Example of utility functions

Question

I am working on an Economics problem and an example function of a graph that looks like this would be helpful. Suppose the straight line is $ax + by = c$, and the curvy lines (called Indifference Curves) are given by the (utility) function $U(x,y)$ when constant.

I need example functions $U(x,y)$ which, when constant, look like the curvy lines.

Note that $t > s > r$.

Answer 1

Experiment with

$$ u(x,y) = r\sin\left(s x\right)\ - tx -y $$