Question: how to dsolve this equation

> test1r := dsolve((Diff(f(x,y), t, t))*x+(Diff(f(x,y), t))*y = 0, f);

 

Error, (in dsolve) expected an ordinary differential equation. Received: 0 = 0

 

another question is

i do not know whether can 

 dsolve((Diff(f(x,y), (x,y), (x,y)))*x+(Diff(f(x,y), (x,y)))*y = 0, f);

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