# Variable substitution in a differential equation

GROUPS:
 In solving an equation, I used a method of variable substitution. Do you think this method is a typical or popular one? In[189]:= (*equation*) In[190]:= eq1 = D[c[r, t], t] == 1/r*D[r*D[c[r, t], r], r] Out[190]= \!$$\*SuperscriptBox[\(c$$, \* TagBox[ RowBox[{"(", RowBox[{"0", ",", "1"}], ")"}], Derivative], MultilineFunction->None]\)[r, t] == ( \!$$\*SuperscriptBox[\(c$$, \* TagBox[ RowBox[{"(", RowBox[{"1", ",", "0"}], ")"}], Derivative], MultilineFunction->None]\)[r, t] + r \!$$\*SuperscriptBox[\(c$$, \* TagBox[ RowBox[{"(", RowBox[{"2", ",", "0"}], ")"}], Derivative], MultilineFunction->None]\)[r, t])/r (*variable substitution at infinity, \ r->R/\[Sigma],t->\[Tau]/(\[Sigma]^2).*) In[196]:= eq5 = eq1 /. {c -> (c1[#1*\[Sigma], #2*\[Sigma]^2] &), r -> (#1/\[Sigma] &[R, \[Tau]]), t -> (#2/\[Sigma]^2 &[R, \[Tau]])} // Simplify // Normal Out[196]= \[Sigma] ( \!$$\*SuperscriptBox[\(c1$$, \* TagBox[ RowBox[{"(", RowBox[{"0", ",", "1"}], ")"}], Derivative], MultilineFunction->None]\)[R, \[Tau]] - ( \!$$\*SuperscriptBox[\(c1$$, \* TagBox[ RowBox[{"(", RowBox[{"1", ",", "0"}], ")"}], Derivative], MultilineFunction->None]\)[R, \[Tau]] + R \!$$\*SuperscriptBox[\(c1$$, \* TagBox[ RowBox[{"(", RowBox[{"2", ",", "0"}], ")"}], Derivative], MultilineFunction->None]\)[R, \[Tau]])/R) == 0