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:
1.
2. ,
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,
or
.
Both will lead to your standard form.