A Treatise on Differential Equations |
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Page xv
... homogeneous functions , 403. The method generalized , 406 . Exercises , 410 . PAGE 381 CHAPTER XVII . SYMBOLICAL METHODS , CONTINUED Symbolical form of differential equations with variable coefficients , 412 . Finite solution , 415-436 ...
... homogeneous functions , 403. The method generalized , 406 . Exercises , 410 . PAGE 381 CHAPTER XVII . SYMBOLICAL METHODS , CONTINUED Symbolical form of differential equations with variable coefficients , 412 . Finite solution , 415-436 ...
Page 34
... homogeneous functions of x and y , and are of the same degree , Thus the equation { y + √ ( x2 + y2 ) } dx − xdy = 0 , is a homogeneous equation , M and N being here of the first degree . To integrate a homogeneous equation it ...
... homogeneous functions of x and y , and are of the same degree , Thus the equation { y + √ ( x2 + y2 ) } dx − xdy = 0 , is a homogeneous equation , M and N being here of the first degree . To integrate a homogeneous equation it ...
Page 35
... homogeneous functions , write M = x " ¿ ( 2 ) , N = x " ↓ ( 2 ) so that the equation Mdx + Ndy = 0 becomes on substitution and division by the common factor x ” , $ ( 2 ) dx + 4 ( 2 ) dy = 0 ..... ..... ( 16 ) . Now assuming y = vx ...
... homogeneous functions , write M = x " ¿ ( 2 ) , N = x " ↓ ( 2 ) so that the equation Mdx + Ndy = 0 becomes on substitution and division by the common factor x ” , $ ( 2 ) dx + 4 ( 2 ) dy = 0 ..... ..... ( 16 ) . Now assuming y = vx ...
Page 60
George Boole. 2ndly . Suppose that one of the functions Mx + Ny and Mx - Ny is ... functions Mx + Ny and Mx - Ny is identically equal to 0 , the reciprocal of ... homogeneous fore if it is a function of y function of x and y of the degree ...
George Boole. 2ndly . Suppose that one of the functions Mx + Ny and Mx - Ny is ... functions Mx + Ny and Mx - Ny is identically equal to 0 , the reciprocal of ... homogeneous fore if it is a function of y function of x and y of the degree ...
Page 61
... homogeneous functions of x and y of a common degree . For let M and N be homogeneous and of the nth degree . Then Mx - Ny and Mx + Ny are each of the degree n + 1 , and Mx - Ny is of the degree 0. Thus Mand Nbeing homogeneous Mx + Ny ...
... homogeneous functions of x and y of a common degree . For let M and N be homogeneous and of the nth degree . Then Mx - Ny and Mx + Ny are each of the degree n + 1 , and Mx - Ny is of the degree 0. Thus Mand Nbeing homogeneous Mx + Ny ...
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