Question: How to pdsolve and exterior derivative a simple one form?

ex1 := {
evalDG( d(x) = w1*e1 + w2*e2),
evalDG(d(e1) = w12*e2 + w13*e3),
evalDG(d(e2) = -w12*e1 + w23*e3),
evalDG(d(e3) = -w13*e1 - w23*e3)
};
ExteriorDerivative(ex1);


> ex1 := {evalDG(d(e1) = w12*e2+w13*e3), evalDG(d(e2) = -w12*e1+w23*e3), evalDG(d(e3) = -w13*e1-w23*e3), evalDG(d(x) = w1*e1+w2*e2)}; ExteriorDerivative(ex1);
{d(e1) = w12 e2 + w13 e3, d(e2) = -w12 e1 + w23 e3, d(e3) = -w13 e1 - w23 e3,

  d(x) = w1 e1 + w2 e2}
Error, (in DifferentialGeometry:-ExteriorDerivative) expected 1st argument to be a differential form. Received: {d(e1) = w12*e2+w13*e3, d(e2) = -w12*e1+w23*e3, d(e3) = -w13*e1-w23*e3, d(x) = w1*e1+w2*e2}


> pdsolve(ex1);
Error, (in pdsolve/sys/info) found functions with same name but depending on different arguments in the given DE system: [d(e1), d(e2)], [d(e2), d(e3)]

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