A Treatise on Differential Equations |
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Page 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 = cx . ( 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 = cx . ( 1 ) , we have on ...
Page 9
... corresponding differential equation will be obtained by mere differentiation and removal of irrelevant factors , i.e. of factors which do not contain and do not therefore affect dy dx ' the relation in which dy dx 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 and do not therefore affect dy dx ' the relation in which dy dx stands to x and y ...
Page 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- dx gents at such points to the axis of x , and definite values of 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- dx gents at such points to the axis of x , and definite values of d'y ...
Page 26
... corresponding finite increment of y , dy dx will represent Ay the limit to which the ratio to 0 . approaches as Ax approaches Ax Let us then first examine the interpretation of the equation M + NAy = 0 ...... Δη ( 2 ) . We have M Δη Δη ...
... corresponding finite increment of y , dy dx will represent Ay the limit to which the ratio to 0 . approaches as Ax approaches Ax Let us then first examine the interpretation of the equation M + NAy = 0 ...... Δη ( 2 ) . We have M Δη Δη ...
Page 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 。= y ...
... 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 。= y ...
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Common terms and phrases
2ndly algebraic arbitrary constant arbitrary function assume C₁ C₂ Cambridge Chap Chapter cloth complete primitive condition Crown 8vo curve deduce determined differential coefficients dp dq dp dy dt dt dv dv dv dx dx dx dy dy dx dz dx² dy dx dy dz dz dx dz dz Edition EDUCATIONAL BOOKS elementary eliminating equa exact differential example expressed fcap finite given equation gives Hence homogeneous functions independent variable integrating factor involving Mdx+Ndy method Mx+Ny obtained ordinary differential equations partial differential equation particular integral primitive equation problem reduced relation represent respect result satisfied second member second order shew singular solution substituting suppose theorem tion transformation TREATISE whence X₁ Y₁ аф
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