A Treatise on Differential Equations, Τόμος 1Macmillan, 1872 - 85 σελίδες |
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Σελίδα 8
... corresponding to the given primitive . If it involve c , then the elimination of c between it and the primitive will lead to the differential equation in question . Thus if the complete primitive be y = = ∞ . ( 1 ) , · we have on ...
... corresponding to the given primitive . If it involve c , then the elimination of c between it and the primitive will lead to the differential equation in question . Thus if the complete primitive be y = = ∞ . ( 1 ) , · we have on ...
Σελίδα 9
... corresponding differential equation will be obtained by mere differentiation and removal of irrelevant factors , i.e. of factors which do not contain dy , and do not therefore affect dy dx dx ' the relation in which stands to x and y ...
... corresponding differential equation will be obtained by mere differentiation and removal of irrelevant factors , i.e. of factors which do not contain dy , and do not therefore affect dy dx dx ' the relation in which stands to x and y ...
Σελίδα 12
... correspond only definite values of the ordinate y determining the corresponding points of the curve , dy definite values of determining the inclination of the tan- gents at such points to the axis of x , and definite values of dx d'y ...
... correspond only definite values of the ordinate y determining the corresponding points of the curve , dy definite values of determining the inclination of the tan- gents at such points to the axis of x , and definite values of dx d'y ...
Σελίδα 26
... corresponding finite increment of the limit to which the ratio Ay to 0 . Ax dy y , will represent dx approaches as Ax approaches Let us then first examine the interpretation of the equation M + N1y Ay = 0 ...... Ax ( 2 ) . We have M Ay ...
... corresponding finite increment of the limit to which the ratio Ay to 0 . Ax dy y , will represent dx approaches as Ax approaches Let us then first examine the interpretation of the equation M + N1y Ay = 0 ...... Ax ( 2 ) . We have M Ay ...
Σελίδα 27
... corresponding to Ax , as the increment of x , it is evident that yo + Ay , will be the value of y corresponding to x + Ax , as the value of x . Representing then this value of y by y , we shall have Y1 = Y 。 + $ ( x 。, y 。) Ax 。= y1 ...
... corresponding to Ax , as the increment of x , it is evident that yo + Ay , will be the value of y corresponding to x + Ax , as the value of x . Representing then this value of y by y , we shall have Y1 = Y 。 + $ ( x 。, y 。) Ax 。= y1 ...
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2ndly algebraic arbitrary constants arbitrary function assume C₁ C₂ Chap Chapter complete primitive condition Crown 8vo curve deduce derived determined differential coefficients dp dp dp dq dp dy dt dt dv du dv dv dv dx dx dx dy dy dx dz dx² dy dx dy dz dz dx dz dy dz dz Edition eliminating equa exact differential expressed fcap finite given equation Hence homogeneous functions independent variable integrating factor involving method Mx+Ny obtained ordinary differential equations P₁ partial differential equation particular integral pdx+qdy primitive equation reduced relation represent respect result satisfied second member second order Shew shewn singular solution substituting suppose theorem tion transformation whence X₁ y₁