ABSTRACT
D + 2kwn+1
(n + 1)(A2 + B2)
dw = Ax + By + C ,
where A, B, C , and D are arbitrary constants (n ≠ –1).
):
w = w(r), r = √
(x + C1)2 + (y + C2)2, whereC1 andC2 are arbitrary constants, and the functionw(r) is determined by the ordinary differential equation
w′′rr + 1 r w′r = kw
5◦. Self-similar solution:
w(x, y) = (x + C1) 2
1-n u(ξ), ξ = y + C2 x + C1
,
where the function u(ξ) is determined by the ordinary differential equation
(1 + ξ2)u′′ξξ – 2(1 + n)
1 – n ξu′ξ +
2(1 + n) (1 – n)2 u – ku
n = 0.
