We consider the partial differential equation

*(rho+nu) V(y,x) == Log(1 / (1 + y (x-y) (beta(psi – D(V(y,x),y)) – eps D(V(y,x),x)))) – eps y (x-y) D(V(y,x),x)*

with the boundary condition

*V(y,y) == 0*

*rho*, *nu*, *beta*, *psi*, *eps* are strictly positive, known constants.

We want to solve for *V(y,x)* over the domain *{(y,x) | y <= x, 0 <= y <= 1, 0.6 <= x <= 1}*.

We pose the following problem to Mathematica:

```
par = {rho -> 0.00014, nu -> 0.00182, psi -> 227.1, beta -> 0.0966, eps -> 0.01};
set = {(rho + nu) V(y, x) == Log(1/(1 + y (x - y) (beta (psi - D(V(y, x), y)) - eps D(V(y, x), x)))) - eps y (x - y) D(V(y, x), x) , V(y, y) == 0} /. par;
Reg = ImplicitRegion((y <= x), {{y, 0, 1}, {x, 0.6, 1}});
NDSolve(set, V, {y, x} ∈ Reg)
```

We get the error message:

```
NDSolve: The arguments should be ordered consistently.
```

We don’t understand this message.

bbgodfrey explains that Mathematica might not be able to solve problems with such a boundary condition. Following bbgodfrey’s suggested approach we therefore try to solve the equation without the boundary condition, using NDSolveValue (because bbgodfrey uses DSolveValue). We pose the problem

```
NDSolveValue((rho + nu) V(y, x) == Log(1/(1 + y (x - y) (beta (psi - D(V(y, x), y)) - eps D(V(y, x), x)))) - eps y (x - y) D(V(y, x), x) /. par, V, {y, x} ∈ Reg)
```

This yields the error message

```
NDSolveValue::femper: PDE parsing error of {0.00196701 V+0.01 V$3966 (x-y) y-Log(1/(1+(Times(<<2>>)+Times(<<2>>)) (x+Times(<<2>>)) y))}. Inconsistent equation dimensions.
```

We are beginners as far as PDEs in Mathematica (and StackExchange) are concerned. Thank you for suggestions on how to proceed.