Đang chuẩn bị nút TẢI XUỐNG, xin hãy chờ
Tải xuống
Handbook of mathematics for engineers and scienteists part 186. 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. | T7.3. Nonlinear Equations 1263 dw X dw X x J2 y dx J dy A separable equation. Complete integral w p x y Ci where the functions p p x and y are determined from the ordinary differential equations Fi x p x C2 F2 y y C2. dw dw x 1 F21 y I aw 0. dx J dy j A separable equation. Complete integral w p x y where the functions p p x and y are determined from the ordinary differential equations Fi x p x ap Ci F2 y ifty ar -Ci where Ci is an arbitrary constant. If a 0 one can set Ci 0 in these equations. 1 dw X 1 dw X x ---- wkFJ y -------- I 0. w dx J w dy j A separable equation. Complete integral w x y p x y . The functions p p x and y are determined by solving the ordinary differential equations p-kFi x p x p C -F2 y y -C where C is an arbitrary constant. 13. Fi fx e F2 y 0. dx J ay j A separable equation. Complete integral w x y p x y . The functions p p x and y are determined by solving the ordinary differential equations e x Fi x p x C ex F2 y y -C where C is an arbitrary constant. 1264 First-Order Partial Differential Equations 1 dw 1 dw x ---- F21 y --------- k ln w. w dx J w dy j A separable equation. Complete integral w x y p x y . The functions p p x and y are determined by solving the ordinary differential eqUatiOnS F1 x pjp - klnp C F2 y tfy - k ln -C where C is an arbitrary constant. 15. 2w yFi x w F2 x w f 0. dx dy J dy J Complete integral w p x y - y F2 x p x dx C1 where the function p x is determined by solving the ordinary differential equation pX. Fi x p 0. 16. F ay 0. dx dy J Complete integral w -axy C1x C2y C3 where F C1 C2 0. 17. dw 2 dw 2 2 2 dw dw O l y y i dx J dy dx dy Complete integral w -C1 arctan 2 J F C1 - C C2 where x2 y2. dw dw dx dy Complete integral w C1 y p x C1 C2 where the function p p x C1 is determined from the ordinary differential equation F x p x C 0. 19. F ax by 2 0. dx dyJ For b 0 see equation T7.3.3.18. Complete integral for b 0 w C1x p z C1 C2 z ax by where the function p p z is determined from the nonlinear ordinary differential
