Making a substitution in an equation

Hi

Can you help me change this equation?

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Hi. Psi function is function of one variable xi, which depends from x,y,t. So, we write explicitly this function , its derivatives and integrals to have finally ODE of one function psi of one variable z. I used z in final equation because xi is defined in Mathematica as function of 3 variables x,y,t.

Thank you I really appreciate your help.