A Treatise on Differential Equations |
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Page 2
... dy dx expressed in terms of x , we might have that differential coefficient expressed in terms of y , or in terms of x and y . Or we might have an equation in which differential coefficients of a higher order , day d3y da das & c ...
... dy dx expressed in terms of x , we might have that differential coefficient expressed in terms of y , or in terms of x and y . Or we might have an equation in which differential coefficients of a higher order , day d3y da das & c ...
Page 4
... dy dx dy dx = C . ( 4 ) , 1+ dy ) 21 3 2 ) dx day dx2 = MX . ( 5 ) . In ( 4 ) the independent variable x , the dependent variable dy y , and the differential coefficient are all involved ; but , dx dy while in the previous examples dx ...
... dy dx dy dx = C . ( 4 ) , 1+ dy ) 21 3 2 ) dx day dx2 = MX . ( 5 ) . In ( 4 ) the independent variable x , the dependent variable dy y , and the differential coefficient are all involved ; but , dx dy while in the previous examples dx ...
Page 6
... d y + 5 dx + 5d8y = sin x , dx2 dg ( 1 − x2 ) dy - - dy X + 4y = cos x , dx the former of which is a linear differential equation with constant coefficients , while the latter would be described as a linear differential equation with ...
... d y + 5 dx + 5d8y = sin x , dx2 dg ( 1 − x2 ) dy - - dy X + 4y = cos x , dx the former of which is a linear differential equation with constant coefficients , while the latter would be described as a linear differential equation with ...
Page 12
... dy day result for y , & c . Thus to a given abscissa of a dx ' dx2 ' given curve , i.e. of a curve determined as to its species by the form of its equation , and as to its elements by the values of the constants in that equation ...
... dy day result for y , & c . Thus to a given abscissa of a dx ' dx2 ' given curve , i.e. of a curve determined as to its species by the form of its equation , and as to its elements by the values of the constants in that equation ...
Page 16
... day the second order , i.e. if they give the same value of dx2 as a function of x , y , and dy , the differential equations of the dx ' dy first order must have originated in the same primitive . Fur- thermore , that primitive will be ...
... day the second order , i.e. if they give the same value of dx2 as a function of x , y , and dy , the differential equations of the dx ' dy first order must have originated in the same primitive . Fur- thermore , that primitive will be ...
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2ndly algebraic arbitrary constant arbitrary function assume C₁ C₂ Cambridge Chap Chapter cloth complete primitive condition Crown 8vo curve deduce determined differential coefficients dp dq dp dy dt dt dv dv dv dx dx dx dy dy dx dz dx² dy dx dy dz dz dx dz dz Edition EDUCATIONAL BOOKS elementary eliminating equa exact differential example expressed fcap finite given equation gives Hence homogeneous functions independent variable integrating factor involving Mdx+Ndy method Mx+Ny obtained ordinary differential equations partial differential equation particular integral primitive equation problem reduced relation represent respect result satisfied second member second order shew singular solution substituting suppose theorem tion transformation TREATISE whence X₁ Y₁ аф
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