Solving uy = -u, Like an ODE Find solutions u = u(x, y) of this PDE. Solution. Settng ux = p, we have Py = -p,| Pu/p = -1, In |p| = -y + õ(x), p= c(x)e¬Y and by integration with respect to x, u (x, y) = f(x)e¬V + 8 (y) where f(x): dx, here, f(x) and g(y) are arbitrary. How p_y=-pI didnt understand this part .

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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How P_y=-P I didnt understand this part .. someone please help.

Solving uy = -u, Like an ODE
Find solutions u =
u (x, y) of this PDE.
Solution. Setting ug = p, we have Py = -p. Py/p = -1, In |p| = -y + x), p= c(x)e¬Y and by
integration with respect to x,
u (x, y) = f(x)e¬Y + g(v)
where
f(x) =
here, f(x) and g(y) are arbitrary.
How p_y=-p I didnt understand this part .
SET 12 =
Transcribed Image Text:Solving uy = -u, Like an ODE Find solutions u = u (x, y) of this PDE. Solution. Setting ug = p, we have Py = -p. Py/p = -1, In |p| = -y + x), p= c(x)e¬Y and by integration with respect to x, u (x, y) = f(x)e¬Y + g(v) where f(x) = here, f(x) and g(y) are arbitrary. How p_y=-p I didnt understand this part . SET 12 =
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