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حول حلول المعادلات التفاضلية الجزئية من الرتبة الثانية ذات المعاملات الثابتة == On Solutions of Partial Differential Equations of Second Order with Constant Coefficients
Author name:
نجوان نوري هاني
Supervisor name:
علي حسن محمد
General topic:
Mathematics
Specific topic:
Mathematics
Degree:
Master
University:
University of Kufa - College Of Education For Girls - Department Of Mathematics
Language:
English
University location:
Najaf
First pages:
27T307 - p.pdf
Abstract:
The main aim of this work is to solve the partial differential equations of second order with constant coefficients which have three independent variables (x , y , t) of the general form : AZ + BZ + CZ + DZ + EZ + FZ +GZ + HZ + IZ + JZ = 0 xx xy xt yy yt tt x y t where A , … , J are real constants . We found that the substitution = ∫ ∫ ∫ U x dx+ V y dy+ W t dt x y t e transforms the above equation to the first order ordinary differential equations with three independent variables which have the general form : F W t W t GU x HV y IW t J A U x U x BU x V y CU x W t D V y V y EV y W t For this purpose , the above partial equation is classified to many cases depending on the values of A, B,K, J . Each case is divided into many other cases , giving the general forms of allcases of the solutions . Some of the solutions are proved , leaving others whose proofs are similar to each other .
