A Treatise on Differential Equations, Volum 1Macmillan, 1872 - 85 sider |
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Resultat 1-5 av 24
Side xiv
... Pdx + Qdy + Rdz = 0 , 272. Condition of derivation from a single primitive , 275. Solution , 276. General rule and ex- amples , 279. Homogeneous equations , 281. Integrating fac- tors , 282. Equations not derivable from a single ...
... Pdx + Qdy + Rdz = 0 , 272. Condition of derivation from a single primitive , 275. Solution , 276. General rule and ex- amples , 279. Homogeneous equations , 281. Integrating fac- tors , 282. Equations not derivable from a single ...
Side 274
... Pdx + Qdy + Rdz = 0 expressed by a single relation be- tween the primitive variables - a relation which with the arbitrary constant of integration will represent a family of surfaces 274 ORDINARY DIFFERENTIAL EQUATIONS [ CH . XII ,
... Pdx + Qdy + Rdz = 0 expressed by a single relation be- tween the primitive variables - a relation which with the arbitrary constant of integration will represent a family of surfaces 274 ORDINARY DIFFERENTIAL EQUATIONS [ CH . XII ,
Side 275
... Pdx + Qdy + Rdz = 0 , derivable from a single primitive . From the given equation , we have P dz = - R Q da - 2 dy . Ꭱ ( 6 ) . But the existence of a single primitive involves the sup- position that z is a function of x and y , and ...
... Pdx + Qdy + Rdz = 0 , derivable from a single primitive . From the given equation , we have P dz = - R Q da - 2 dy . Ꭱ ( 6 ) . But the existence of a single primitive involves the sup- position that z is a function of x and y , and ...
Side 276
... Pdx + Qdy + Rdz = 0 when the equation of condition ( 8 ) is satisfied . The supposed primitive involving all the variables æ , y , z , it is evident that if we differentiate it on the hypothesis that z is constant , we shall arrive at a ...
... Pdx + Qdy + Rdz = 0 when the equation of condition ( 8 ) is satisfied . The supposed primitive involving all the variables æ , y , z , it is evident that if we differentiate it on the hypothesis that z is constant , we shall arrive at a ...
Side 281
... Pdx + Qdy + Rdz = 0 is homoge- neous with respect to x , y , z , its solution will be facilitated by a transformation similar to that employed for homogeneous equations with two variables . Assuming x = uz , y = vz , we obtain by ...
... Pdx + Qdy + Rdz = 0 is homoge- neous with respect to x , y , z , its solution will be facilitated by a transformation similar to that employed for homogeneous equations with two variables . Assuming x = uz , y = vz , we obtain by ...
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A Treatise on Differential Equations: Supplementary Volume George Boole Uten tilgangsbegrensning - 1865 |
Vanlige uttrykk og setninger
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