A Treatise on Differential Equations, Τόμος 1Macmillan, 1872 - 85 σελίδες |
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Σελίδα 2
... expression of which a differential coefficient is involved . But instead of having as in that example expressed in terms of dy dx x , we might have that differential coefficient expressed in terms of y , or in terms of x and y . Or we ...
... expression of which a differential coefficient is involved . But instead of having as in that example expressed in terms of dy dx x , we might have that differential coefficient expressed in terms of y , or in terms of x and y . Or we ...
Σελίδα 19
... expression is of a more absolute character than that of the previous equation ( 6 ) . For in that equation we may ... expressed by the algebraic equation ax2 + bxy + cy2 + ex + fy = 1 . It is 3 9 ( de ) d'y - 45 2-2 ART . 11. ] 19 ...
... expression is of a more absolute character than that of the previous equation ( 6 ) . For in that equation we may ... expressed by the algebraic equation ax2 + bxy + cy2 + ex + fy = 1 . It is 3 9 ( de ) d'y - 45 2-2 ART . 11. ] 19 ...
Σελίδα 28
... expression of that law will be the solution of the differential equation given . 3. To illustrate the same doctrine geometrically , if x and y ... expressed by ( 6 ) . u = c , dx + dy dx = 0 28 [ CH . II . DIFFERENTIAL EQUATIONS OF THE.
... expression of that law will be the solution of the differential equation given . 3. To illustrate the same doctrine geometrically , if x and y ... expressed by ( 6 ) . u = c , dx + dy dx = 0 28 [ CH . II . DIFFERENTIAL EQUATIONS OF THE.
Σελίδα 37
... expressed ax + by + ac ) dy = 0 , ( ax + by + c ) dx + a ( ax + by + α and the variables will be separated if we assume ax + by = 2 , and then adopt either z and x or z and y as the new variables . These transformations are linear , and ...
... expressed ax + by + ac ) dy = 0 , ( ax + by + c ) dx + a ( ax + by + α and the variables will be separated if we assume ax + by = 2 , and then adopt either z and x or z and y as the new variables . These transformations are linear , and ...
Σελίδα 52
... expression of the form f ( u ) du which is necessarily an exact differential . 1 Ex . Given { + √ ( ) } da + { y − y + ... expressed in the form of the product y √ ( y2 — x2 ) X - yd — xảy y2 1 the second factor of which is the ...
... expression of the form f ( u ) du which is necessarily an exact differential . 1 Ex . Given { + √ ( ) } da + { y − y + ... expressed in the form of the product y √ ( y2 — x2 ) X - yd — xảy y2 1 the second factor of which is the ...
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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