tailieunhanh - Handbook of mathematics for engineers and scienteists part 184

Handbook of mathematics for engineers and scienteists part 184. Tài liệu toán học quốc tế để phục vụ cho các bạn tham khảo, tài liệu bằng tiếng anh rất hữu ích cho mọi người. | . Linear Equations 1249 4. adW bdW f x g y dx dy General solution a y f x dx 1 g y dy bx - ay . w 5. tt adw f x 9 y . dx dy General solution w f t g y - ax at dt y - ax where x0 can be taken dxQ arbitrarily. 6. adw f x y . ox dy General solution w f t y -ax at dt y -ax where x0 can be taken arbitrarily. dxQ 7. dT ay f x dT 9 x . ox dy General solution w J g x dx u where u e axy - J f x e ax dx. 8. y ay f x g x h y . ox dy General solution w y g x h eaxu eax J f x e ax dx dx u where u e axy - J f x e ax dx. In the integration u is treated as a parameter. dw r dw 9. dx f x y 9 x yk dy h x . General solution w J h x dx u where u e F y1 k e Fg x dx F 1 -k J f x dx. dw r . dw 10 dx f x 9 x eXv dy h x . General solution w J h x dx u where u e XyF x J g x F x dx F x exp Jf x dx . 1250 First-Order Partial Differential Equations H- axdw bydr f x y . ox oy General solution w 1 f x u1 ax f dx u where u yax b. In the integration u is treated as a parameter. 12- f x d g y r fa x h-2 y . ox oy General solution w bix dx y dy J f x J g y y 13. f x g y h x y . ox oy dx dx f dy n ---leads to an equation of the form for f x J g y w w n . 14- f y y 9 x h x y . ox oy The transformation J g x dx n J f y dy leads to an equation of the form for w w n . . Equations of the Form f x 11 a x 11 h x ii w r x ti J x y dx g x y dy l x y w x y In the solutions of equations z is an arbitrary composite function whose argument z can depend on both x and y. 1. a W b W f x w. C _ Cï J ax ay General solution w exp f x dx bx - ay . 2. ay- b f x w g x ox oy General solution w exp 1 f x dx a J bx - ay g x exp a 3. adw bdw f x g y w. ox oy General solution w exp f x dx by g y dy bx - ay . . Linear Equations 1251 4. y a f x y w. ox oy x General solution w exp - ax at dt y - ax where x0 can be taken arbitrarily. Xo 5- dW a W f x y w g x y . ox oy General solution w F x u u g x u ax F x u dx F x u exp f x u ax dx where u y - ax. In the integration u is treated

TỪ KHÓA LIÊN QUAN
crossorigin="anonymous">
Đã phát hiện trình chặn quảng cáo AdBlock
Trang web này phụ thuộc vào doanh thu từ số lần hiển thị quảng cáo để tồn tại. Vui lòng tắt trình chặn quảng cáo của bạn hoặc tạm dừng tính năng chặn quảng cáo cho trang web này.