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**From PDE to ODE ?! + research**

## Homework Statement

In the attached research, What are the steps that we work to transform the equation (1) to (8)

## Homework Equations

(1) and (8)

## The Attempt at a Solution

I know that they used similarity transformations but I do not know how to do it by myself (how to substitute correctly) ...

can you help me to I understand the steps ... then I will do the others In the same way.

Thanks