A Treatise on Differential Equations |
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Page 41
... dz dryi dry , dc + Σ + dx + 1 di dx dx = Σci dryi + Σ ¡ d'y i dx + 1 dx X1 ) dz X ; z + dx dci on substituting for the value X as above determined . dx stitute as above for dci dx ' We observe that the coefficient of z is here a known ...
... dz dryi dry , dc + Σ + dx + 1 di dx dx = Σci dryi + Σ ¡ d'y i dx + 1 dx X1 ) dz X ; z + dx dci on substituting for the value X as above determined . dx stitute as above for dci dx ' We observe that the coefficient of z is here a known ...
Page 42
... dmy dxm = dm yi Σci dxm from m = 0 to m = n- 2 , then 7n - 1 dn - 1y dxn - 1 = Σα dx - 1 i +29 Yi dy = Σc dy + ( x dry ) = + dz . dx " dx - 1 dx Accordingly the differential equation for z will be dz dx 42 [ CH . XXII . ADDITIONS TO CHAPTER ...
... dmy dxm = dm yi Σci dxm from m = 0 to m = n- 2 , then 7n - 1 dn - 1y dxn - 1 = Σα dx - 1 i +29 Yi dy = Σc dy + ( x dry ) = + dz . dx " dx - 1 dx Accordingly the differential equation for z will be dz dx 42 [ CH . XXII . ADDITIONS TO CHAPTER ...
Page 43
George Boole. Accordingly the differential equation for z will be dz dx + ΣΧ = dx2 - 1 Now the equations for determining dc , dc2 dcn - 1 " dx dx .... dx dci become on putting X , for det , and writing for brevity y ' ; for dx dyi day ...
George Boole. Accordingly the differential equation for z will be dz dx + ΣΧ = dx2 - 1 Now the equations for determining dc , dc2 dcn - 1 " dx dx .... dx dci become on putting X , for det , and writing for brevity y ' ; for dx dyi day ...
Page 44
... dx Hence ΣΧΥ ( -1 ) = Σ 1 dM M dy ( " ~ 2 ) Y ( " ~ 1 ) = 1 dM M dx Thus the equation ( 7 ) becomes dz dM de + ( 1 do +4 , ) == X ; dx 1 therefore z = € M M dx dx 1 dM Hence , since dci = X1z = dx 44 [ CH . XXII . ADDITIONS TO CHAPTER IX .
... dx Hence ΣΧΥ ( -1 ) = Σ 1 dM M dy ( " ~ 2 ) Y ( " ~ 1 ) = 1 dM M dx Thus the equation ( 7 ) becomes dz dM de + ( 1 do +4 , ) == X ; dx 1 therefore z = € M M dx dx 1 dM Hence , since dci = X1z = dx 44 [ CH . XXII . ADDITIONS TO CHAPTER IX .
Page 45
George Boole. 1 dM Hence , since dci = X1z = dx 1 whence - we have Mdy ( n - 2 ) 2 , dM M dy ( " - 2 ) 1 dM M zdx , y = 2y . 31 dy , dz , z being given above . In the case of X = 0 , we have 2 = C whence y = = C ᏧᎷ € -SA1dx dx . M2 dy ...
George Boole. 1 dM Hence , since dci = X1z = dx 1 whence - we have Mdy ( n - 2 ) 2 , dM M dy ( " - 2 ) 1 dM M zdx , y = 2y . 31 dy , dz , z being given above . In the case of X = 0 , we have 2 = C whence y = = C ᏧᎷ € -SA1dx dx . M2 dy ...
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Common terms and phrases
arbitrary constants Cambridge Chap Chapter College complete primitive condition Crelle's Journal Crown 8vo deduce derived determine dF dF dF dF dF dF dp dF dx dFdF differential coefficients dp dF dp dp dx dp dq dp dy dp₁ dq dp dv dv dx dp dp dx dx dx dy dy dx dz dx₁ dx² dy dp dy dx dy dz dz dy dz dz Edition eliminate equa Eton College expression Extra fcap factor function given equation Hence J. P. MAHAFFY Jacobi Last Multiplier linear partial differential m₁ memoir ordinary differential equations Owens College P₁ partial differential equations particular integral Professor Boole reduced represent result revised School shewn singular solution system of ordinary theorem theory tion transformation u₁ u₂ values vanish whence X₁ Y₁ аф
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