Solutions for certain classes of the Riccati differential equation

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Atıf İçin Kopyala

Saad N., Hall R. L., Ciftci H.

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, cilt.40, sa.35, ss.10903-10914, 2007 (SCI-Expanded)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 40 Sayı: 35
• Basım Tarihi: 2007
• Doi Numarası: 10.1088/1751-8113/40/35/012
• Dergi Adı: JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
• Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Sayfa Sayıları: ss.10903-10914
• Gazi Üniversitesi Adresli: Evet

Özet

We derive some analytic closed-form solutions for a class of Riccati equations y'(x) - lambda(0)(x) y(x) +/- y(2)(x) = +/- s(0)(x) where lambda(0)( x), s(0)( x) are C-infinity- functions. We show that if delta(n) = lambda(n)s(n-1) - lambda(n-1)s(n) = 0, where lambda(n) = lambda(')(n-1) + s(n-1) + lambda(0)lambda(n-1) and s(n) = s(n-1)(')+ s(0)lambda(k-1) , n = 1, 2, ... , then the Riccati equation has a solution given by y( x) = -/+ s(n-1)(x)/ lambda(n-1)(x). Extension to the generalized Riccati equation y'(x) + P(x) y(x) + Q(x) y(2)(x) = R(x) is also investigated.