uxx + 4 cos(2x)uxy - 4 sin2(2x)uyy - 4 sin(2x)uy = 0.
Å„Å‚
òÅ‚¾ = y - 2x - sin(2x)
ół· = y + 2x - sin(2x)
Å„Å‚
òÅ‚s = ¾ + ·
vss - vtt = 0
ółt = ¾ - ·
2y
4y2uxx + 2(1 - y2)uxy - uyy - (2ux - uy) = 0.
1+y2
Å„Å‚
òÅ‚¾ = 2y3 - 3x
ół· = x + 2y
v¾· = 0 v¾· = 0
2y
4y2uxx + 2(1 - y2)uxy - uyy - (2ux - uy) = 0 u(x, 0) = x, uy(x, 0) = 2x.
1+y2