A Treatise on Differential Equations, Τόμος 1Macmillan, 1872 - 85 σελίδες |
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Σελίδα vii
... dependent upon the performance of certain inverse operations . I have endeavoured to shew in Chap . XVI . , that the expressions by which these inverse operations are sym- bolized are in reality a species of interrogations , admitting ...
... dependent upon the performance of certain inverse operations . I have endeavoured to shew in Chap . XVI . , that the expressions by which these inverse operations are sym- bolized are in reality a species of interrogations , admitting ...
Σελίδα xiii
... Dependent class , 203. Properties of linear Analogy with Algebraic equations , 206. Exer- CHAPTER X. EQUATIONS OF AN ORDER HIGHER THAN THE FIRST , CONTINUED One variable wanting , 209. One differential coefficient present , 211 . dry ...
... Dependent class , 203. Properties of linear Analogy with Algebraic equations , 206. Exer- CHAPTER X. EQUATIONS OF AN ORDER HIGHER THAN THE FIRST , CONTINUED One variable wanting , 209. One differential coefficient present , 211 . dry ...
Σελίδα 3
... dependent , x and y for its independent variables . The dz dz equation x = z is a partial differential equation . dx + y dy The present chapter will be chiefly devoted to the con- sideration of that class of ordinary differential ...
... dependent , x and y for its independent variables . The dz dz equation x = z is a partial differential equation . dx + y dy The present chapter will be chiefly devoted to the con- sideration of that class of ordinary differential ...
Σελίδα 4
... dependent variable dy dx and the differential coefficient are all involved ; but , dy while in the previous examples appears only in the first dx degree , in the present one it appears in the second degree and under a radical sign . In ...
... dependent variable dy dx and the differential coefficient are all involved ; but , dy while in the previous examples appears only in the first dx degree , in the present one it appears in the second degree and under a radical sign . In ...
Σελίδα 6
... dependent and independent ; such reference being established through the medium of differential coefficients . Now the chief object of the study of differential equations is to enable us to determine whenever it is possible , and in the ...
... dependent and independent ; such reference being established through the medium of differential coefficients . Now the chief object of the study of differential equations is to enable us to determine whenever it is possible , and in 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