I know Thevenin equivalents but only the basics and I don't know how to use it in that circuit. All I did was simplify the circuitYou said you did what you can, but then don't show what you did. We aren't mind readers. Show your work.
You have this "U1" marked but don't give its polarity?
Is your dependent source a dependent voltage source or a dependent current source?
What are the units of the parameters in your nonlinear element? Is it 5 A² ? Is it 3 V/mA² ?
Are you familiar with Thevenin equivalents?
Are you familiar with load line analysis?