A Treatise on Differential Equations, Τόμος 1Macmillan, 1872 - 85 σελίδες |
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Σελίδα xiii
... equa . tions , 215. Exact equations , 222. Miscellaneous methods and examples , 226. Singular integrals , 229. Exercises , 234 . CHAPTER XI . GEOMETRICAL APPLICATIONS Different problems , 239-244 . Trajectories , 245. Curves of Pursuit ...
... equa . tions , 215. Exact equations , 222. Miscellaneous methods and examples , 226. Singular integrals , 229. Exercises , 234 . CHAPTER XI . GEOMETRICAL APPLICATIONS Different problems , 239-244 . Trajectories , 245. Curves of Pursuit ...
Σελίδα 6
... Equa- tions ( 1 ) , ( 2 ) and ( 3 ) are thus seen to be linear , but ( 4 ) and ( 5 ) are not linear . If we refer ( 3 ) , after dividing both members by x2 , to the general form ( 10 ) , we have n = 2 , X , 1 = -1 , X , = -1 ;, X = sin ...
... Equa- tions ( 1 ) , ( 2 ) and ( 3 ) are thus seen to be linear , but ( 4 ) and ( 5 ) are not linear . If we refer ( 3 ) , after dividing both members by x2 , to the general form ( 10 ) , we have n = 2 , X , 1 = -1 , X , = -1 ;, X = sin ...
Σελίδα 10
... equa- tion containing x and y with an arbitrary constant c , we can by differentiation , and elimination ( if necessary ) of that con- stant , obtain the differential equation of the first order , of which the given equation constitutes ...
... equa- tion containing x and y with an arbitrary constant c , we can by differentiation , and elimination ( if necessary ) of that con- stant , obtain the differential equation of the first order , of which the given equation constitutes ...
Σελίδα 13
... equa- tion multiplied by b , we have d'y dxx − ( a + b ) dy + aby = 0. ... .. - - the differential equation of the second order required . . ( 11 ) , If we had first eliminated c ' we should in the place of ( 10 ) have obtained the ...
... equa- tion multiplied by b , we have d'y dxx − ( a + b ) dy + aby = 0. ... .. - - the differential equation of the second order required . . ( 11 ) , If we had first eliminated c ' we should in the place of ( 10 ) have obtained the ...
Σελίδα 15
... equa- tions r + 1 only will be independent . C 2nd . There will exist one differential equation of the nth order free from arbitrary constants . The converse of the latter truth , viz . that a differential equation of the nth order ...
... equa- tions r + 1 only will be independent . C 2nd . There will exist one differential equation of the nth order free from arbitrary constants . The converse of the latter truth , viz . that a differential equation of the nth order ...
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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