A Treatise on Differential Equations, Volume 1 |
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... second order in Ex . 31 is required . 34. A first integral of the differential equation of the x2 - - - 2 second order y ― xy , + 2 Y2 − ( Y1 — xy , ) 2 — y22 = 0 is y - xy1 y + - ( ~ 1 — a3 ) a2 x- ( 1- -- · 2a ) xy , -a2 - y , 2 = 0 ...
... second order in Ex . 31 is required . 34. A first integral of the differential equation of the x2 - - - 2 second order y ― xy , + 2 Y2 − ( Y1 — xy , ) 2 — y22 = 0 is y - xy1 y + - ( ~ 1 — a3 ) a2 x- ( 1- -- · 2a ) xy , -a2 - y , 2 = 0 ...
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... second order . 37. The same singular integral has for its singular solution 16y + 4x2 + x * = 0. Prove this . Have we a right to expect that this will satisfy the differential equation of the second order ? 38. By reasoning similar to ...
... second order . 37. The same singular integral has for its singular solution 16y + 4x2 + x * = 0. Prove this . Have we a right to expect that this will satisfy the differential equation of the second order ? 38. By reasoning similar to ...
Page viii
... second order given in Chap . XV . With respect to the sources from which information has been drawn , it is proper to mention that , on questions re- lating to the theory of differential equations , my obligations are greatest to ...
... second order given in Chap . XV . With respect to the sources from which information has been drawn , it is proper to mention that , on questions re- lating to the theory of differential equations , my obligations are greatest to ...
Page ix
... second order , and , as has already been intimated , to symboli- cal methods . The demonstrations scattered through the work are also many of them new , at least in form . In recent years much light has been thrown on certain classes of ...
... second order , and , as has already been intimated , to symboli- cal methods . The demonstrations scattered through the work are also many of them new , at least in form . In recent years much light has been thrown on certain classes of ...
Page xiii
... ORDER HIGHER THAN THE FIRST • PAGE 139 • · 187 Relation to complete primitive , 187. Solution by development , 189 . Linear equations , 192-199 . General rule when the second Second member a function of x , -Variation Dependent class ...
... ORDER HIGHER THAN THE FIRST • PAGE 139 • · 187 Relation to complete primitive , 187. Solution by development , 189 . Linear equations , 192-199 . General rule when the second Second member a function of x , -Variation Dependent class ...
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Common terms and phrases
2ndly algebraic arbitrary constant arbitrary function assume C₁ C₂ Cambridge Chap Chapter College complete primitive condition corresponding Crown 8vo curve deduce degree derived determined differential coefficients dp dy dv dv dx dx dx dy dy dx dz dx² dy dx dy dz dz dx dz dz Edition eliminating equa exact differential expressed Extra fcap fcap finite given equation Hence homogeneous functions Illustrations independent variable infinite integrating factor involving Mdx+Ndy method Mx+Ny obtained ordinary differential equations P₁ partial differential equation particular integral primitive equation Professor Prop reduced relation represent respect result satisfied second member second order Shew singular solution substituting suppose Taylor's theorem theorem tion transformation V₁ whence y₁ аф
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