Question: how to pdsolve this ?

why system inconsistent 

when only want to obtain a equation H

in terms of a1 , a3, b2, b3, c1, c2, x1, x2, lambda

pdsolve([
Diff(H(x1,x2,lambda), x1) = a1*x1 + a3*lambda,
Diff(H(x1,x2,lambda), x2) = b2*x2 + b3*lambda,
Diff(H(x1,x2,lambda), lambda) = c1*x1 + c2*x2
], H(x1,x2,lambda));

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