In this case, the PDE evaluates to have a higher-than-first-order derivative depending on the dependent variable:

The solution in this case is to use a formal PDE:

More information can be found in the Finite Element Usage Tips tutorial.

Consider the equation with boundary conditions and for this example :

To solve, rewrite the equation in inactive form to :

Compute the solution to a less nonlinear problem ():

Use the computed solution of the less nonlinear problem () as an initial seed to solve the original equation ():

Nonlinear PDE coefficients with higher-than-first-order derivatives depending on the dependent variable cannot be solved in this version of NDSolve: