Actually there are only 3 variables M1, M2, M3, but

M:=Matrix(3, 3, symbol=m);  have 9 variables, though multiplication of matrix is correct, how to solve?

After tried Solve command, it can not solve to a correct answer.

@Preben Alsholm t is just a variable

sorry for typing mistake, but FAILED result is the problem, the paper said a transformation can make it work, taylor(ln(a series)), how this work? would you mind demonstrating it with this example?

Do this multivariable function have PDE?

i just want to guess a PDE whose solution is this multivariable function?

Any method to check it whether it have PDE?

I am afraid of trying all combination of PDE and guess all coefficients to find back its PDE

initial condition come from one function should be consistent

i use maple 12, all get the same error

f1 := ln(1-x1*x2-c*x1/2)/x1;
subs({x1=1,x2=x2},f1);
subs({x1=x1,x2=0},f1);

motion := {diff(h(x1,x2), x1, x1) + 2*diff(h(x1,x2), x1, x2) + diff(h(x1,x2), x2, x2) = 0};
ic := {h(1,0)=ln(1-(1/2)*c)};
monster := pdsolve(motion union ic);

motion := {diff(h(x1,x2), x1) + exp(x1*x2)*diff(h(x1,x2), x2) = 0};
ic := {h(1,0)=ln(1-(1/2)*c)};
monster := pdsolve(motion union ic);

typing error , only this l := [0,0,0,2,0,0,0,0,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,0,1,0,2,0,0,0,1,0,0,0,0,0,1,1,0,1,1]:
is fail