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How can you change 

f[g[x,t],t]

to

f[g,t]

?

I have differential equations

Derivative[1,0][f][g[x,t],t]== f[g[x,t],t]*t+Derivative[2,0]f[g[x,t],t]

And 

f'[g[x,t]]== f[g[x,t]]*t+f''[g[x,t]]

And I'd like to use DSolve with $g$ as an independant variable, meaning : 

DSolve[Derivative[1,0][f][g,t]== f[g,t]*t+Derivative[2,0]f[g,t],f,{g,t}]

I tried : 

(f'[g[x,t]]== f[g[x,t]]*t+f''[g[x,t]])/.g[x,t]-> g

but it failed

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  • $\begingroup$ If you are only dealing with a single example with the same variables, the easiest way is to just use Find and Replace. $\endgroup$ – kickert Aug 8 '19 at 14:22
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f[g[x,t],t] /. g[___]->g
(*    f[g, t]    *)
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put bracket around f in the Derivative-commands f -> [f]:

Derivative[1, 0][f][g[x, t], t] ==f[g[x, t], t]*t + Derivative[2, 0][f][g[x, t], t]
(*\!\(\*SuperscriptBox[\(f\), TagBox[RowBox[{"(", RowBox[{"1", ",", "0"}], ")"}],Derivative],MultilineFunction->None]\)[g, t] == t f[g, t] + \!(\*SuperscriptBox[\(f\), TagBox[RowBox[{"(", RowBox[{"2", ",", "0"}], ")"}],Derivative],MultilineFunction->None]\)[g, t]*)
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