solve-the-EDP-1-x-f-x-y-f-y-0-2-x-f-x-f-y-z-2-x-3-x-2-2-f-x-2-y-2-2-f-y-2-0-

Question Number 198355 by lapache last updated on 18/Oct/23

s o l v e t h e E D P

1 - x \frac{\partial f}{\partial x} - y \frac{\partial f}{\partial y} = 0

2 - x \frac{\partial f}{\partial x} - \frac{\partial f}{\partial y} = \frac{z^{2}}{x}

3 - x^{2} \frac{\partial^{2} f}{\partial x^{2}} - y^{2} \frac{\partial^{2} f}{\partial y^{2}} = 0

Commented by Gracetestifier last updated on 18/Oct/23

p l e a s e p o s t t h e a n s w e r w h e n i t i s r e a d y

Commented by mokys last updated on 18/Oct/23

2 - \frac{d x}{x} = \frac{d y}{- 1} = \frac{x d z}{z^{2}}

[\frac{d x}{x} = - \frac{d y}{1}] \to l n x + y = a

[\frac{d x}{x} = \frac{x d z}{z^{2}}] \to \frac{d x}{x^{2}} = \frac{d z}{z^{2}} \to \frac{1}{z} - \frac{1}{x} = b

f (a, b) = 0 \to f (l n x + y, \frac{1}{z} - \frac{1}{x}) = 0

Facebook Tweet Pin