Hi, I am having difficulty doing these 2 questions. I tried the change of coordinates but that got very messy and got me nowhere.
Reduce to canonical form:
Thanks for your help.
For the first one, since , then the PDE is parabolic and the normal or standard form is . Substitute the change of variables in and collect about the like higher or terms (i.e. ). Setting the coefficient of and gives
This we solve giving Now can be as anything involving and can be chosen as really anything provided that . For example,
Both will lead to your standard form.