partial diff equation: transform equations to canonical form

[A_Helal]

my question
partial diff equation
and
i need all steps
question :

\(\displaystyle \mbox{ Transform to canonical form:}\)

\(\displaystyle 1.\, e^{2y}\, \dfrac{\partial^2u(x,\, y)}{\partial x^2}\, -\, 4x^2\, \dfrac{\partial^2 u(x,\, y)}{\partial y^2}\, =\, 0\)

\(\displaystyle 2.\, x^2\, \dfrac{\partial^2 u(x,\,y)}{\partial x^2}\, +\, y^2\, \dfrac{\partial^2 u(x,\, y)}{\partial y^2}\, =\, 0\)

 

[stapel]

i need all steps

I'm sorry, but "all steps" is kinda your job, like you saw in the "Read Before Posting" thread that you read before posting.

question :

\(\displaystyle \mbox{ Transform to canonical form:}\)

\(\displaystyle 1.\, e^{2y}\, \dfrac{\partial^2u(x,\, y)}{\partial x^2}\, -\, 4x^2\, \dfrac{\partial^2 u(x,\, y)}{\partial y^2}\, =\, 0\)

\(\displaystyle 2.\, x^2\, \dfrac{\partial^2 u(x,\,y)}{\partial x^2}\, +\, y^2\, \dfrac{\partial^2 u(x,\, y)}{\partial y^2}\, =\, 0\)

To get started, please provide the volunteers with your understanding of what "canonical form" means in this context? If you have made any attempts, please include this information too, even if you think it is wrong. Thank you!