# Rules Being Ignored by Mathematica

Can someone explain to me why Mathematica is ignoring the replacement rules in the following code:

eq = D[ψ[x, y], y] D[ψ[x, y], {y, 2}, {x}] - D[ψ[x, y], x] D[ψ[x, y], {y, 3}] == D[ψ[x, y], {y, 4}];
eq1 = eq /. {ψ[x, y] -> x^α f[η[x, y]], η[x, y] -> y x^-β}
eq2 = eq1 /. {α -> 1/2, β -> 1/2}


Basically, I have a fourth order PDE and I want to define a similarity transformation to reduce it to a third-order ODE. Previously when I ran this, the second command was outputting something in terms of the function f and the variable \eta. However, when I now run this it is just ouputting the exact thing as eq. I don't understand the issue at all. I have tried using various clear commands, but that doesn't seem to be the issue.

As an aside, these are three lines of code in a larger notebook. However, even when I copy and past them into a different notebook the issue persists.

• ReplaceAll works on the full form of an expression, not on what is displayed. To see the full form, use: FullForm. Commented Mar 8 at 19:41
• Look at result of InputForm@eq. Your replacement patterns do not exist in eq. Commented Mar 8 at 19:42
• Does that mean I need to substitute this into the equation and actually calculate the new derivatives by hand? Commented Mar 8 at 19:42
• Yesterday though it was outputting something in terms of the function f. And then when I gave it specific values of alpha and beta it was also putting that in without issue. Commented Mar 8 at 19:43
• Did you try eq1 = eq /. {\[Eta] -> Functon[{x, y}, y x^-\[Beta]], \[Psi] -> Function[{x, y}, x^\[Alpha] f[\[Eta][x, y]]]}? Commented Mar 8 at 19:47

    eq1 = eq //.

$$x^{2 \alpha -3 \beta -1} \left((\alpha -2 \beta ) f'\left(y x^{-\beta }\right) f''\left(y x^{-\beta }\right)-\alpha f\left(y x^{-\beta }\right) f^{(3)}\left(y x^{-\beta }\right)\right)=x^{\alpha -4 \beta } f^{(4)}\left(y x^{-\beta }\right)$$