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