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Handbook of mathematics for engineers and scienteists part 4

This function is defined for all x e 11. +3c). and its range consists of y e [0, +30). The arccosh 3; is neither odd nor even; it is nonperiodic and unbounded. It does not cross the axis Oy and crosses the axis Ox at the point j1 = 1. It is an increasing function in its domain with the minimal value y = 0 at x = 1. The graph of the function y = arccosh x is given in Fig. 2.19. | Contents xxi T5. Ordinary Differential Equations.1207 T5.1. First-Order Equations.1207 T5.2. Second-Order Linear Equations.1212 T5.2.1. Equations Involving Power Functions .1213 T5.2.2. Equations Involving Exponential and Other Functions.1220 T5.2.3. Equations Involving Arbitrary Functions.1222 T5.3. Second-Order Nonlinear Equations.1223 T5.3.1. Equations of the Form y x f x y .1223 T5.3.2. Equations of the Form f x y yxx g x y y x .1225 References for Chapter T5.1228 T6. Systems of Ordinary Differential Equations .1229 T6.1. Linear Systems of Two Equations .1229 T6.1.1. Systems of First-Order Equations .1229 T6.1.2. Systems of Second-Order Equations . 1232 T6.2. Linear Systems of Three and More Equations.1237 T6.3. Nonlinear Systems of Two Equations . 1239 T6.3.1. Systems of First-Order Equations .1239 T6.3.2. Systems of Second-Order Equations .1240 T6.4. Nonlinear Systems of Three or More Equations .1244 References for Chapter T6.1246 T7. First-Order Partial Differential Equations .1247 T7.1. Linear Equations . 1247 T7 11 Equations of the Form f x ru u x ru 0 1247 a . a.a. t- qu ttuns oa me t oun j y x y dx g x y dy . T7 12 Eiuations of the Form f x 7 a x 11 h x 7 1248 a t . a. . j_ qu- t ia aaas aa me a aaaaa j y x y j q i g x x y j q i v y x y j .a j T7 13 Equations of the Form f x 7 n x n dw h x i Sw r x 7 1250 A . A.O. A qu tAOns oA tAAe A oAAAA y x y y dx g x y y dy x y y w I y y . A T7.2. Quasilinear Equations .1252 T7 2 1 Equations of the Form f x 7 n x 7 h x 7 w 1252 A . . A. J qu l LAons ot tAAe A AAAAA J y x y Q I g x y y Q v x y Wy .A T7 2 2 Equations of the Form f x n w w 0 1254 A . . . A qu tAOns oA tAAe A oA A dx A y Wy dy J.A O i T7 2 3 Equations of the Form f x n w @w a x n w 1256 A I . .O . A qu tAOns oA tAAe A oA A dx A x.x y wj dy - y wj . A T7.3. Nonlinear Equations . 1258 T7.3.1. Equations Quadratic in One Derivative .1258 T7.3.2. Equations Quadratic in Two Derivatives .1259 T7.3.3. Equations with Arbitrary Nonlinearities in Derivatives . .