A Treatise on Differential Equations, Volum 1Macmillan, 1872 - 85 sider |
Inni boken
Resultat 1-5 av 81
Side 39
... Hence Spax Q. dx Therefore C = ! = √ εSP2 Qdx + C , .. c being an arbitrary constant . Substituting this generalized value of C'in ( 22 ) , we have finally y = eTrix ( Se Srix Qdx + the solution required . c ) ( 23 ) , It will be ...
... Hence Spax Q. dx Therefore C = ! = √ εSP2 Qdx + C , .. c being an arbitrary constant . Substituting this generalized value of C'in ( 22 ) , we have finally y = eTrix ( Se Srix Qdx + the solution required . c ) ( 23 ) , It will be ...
Side 40
... Hence Spai Q = ( x + 1 ) 3 . x + 1 ' € Srax = ( x [ Pdx = -2 log ( x + 1 ) , ( 28 + 1 ) ~ " . Je Qdx = + 2 ( x 1 ) 2 + c . 1 ) " + c } . Setra Que = f ( x + 1 ) dx ( ( x 1 ) 2 y = ( x + 1 ) ( * + Therefore Ex . 2. Given dy ny dx x + 1 = 2 ...
... Hence Spai Q = ( x + 1 ) 3 . x + 1 ' € Srax = ( x [ Pdx = -2 log ( x + 1 ) , ( 28 + 1 ) ~ " . Je Qdx = + 2 ( x 1 ) 2 + c . 1 ) " + c } . Setra Que = f ( x + 1 ) dx ( ( x 1 ) 2 y = ( x + 1 ) ( * + Therefore Ex . 2. Given dy ny dx x + 1 = 2 ...
Side 43
... Hence M and N being given , the expressions for are implicitly given also . dy d'y Now dx ' dx2 > dy dy dx ' dx2 & c ... Hence & ( x ) = y 。· Again , o ' ( x ) is what dy dp ( x ) i . e . becomes when x = x 。• > dx dx ' Hence ' ( x ) ...
... Hence M and N being given , the expressions for are implicitly given also . dy d'y Now dx ' dx2 > dy dy dx ' dx2 & c ... Hence & ( x ) = y 。· Again , o ' ( x ) is what dy dp ( x ) i . e . becomes when x = x 。• > dx dx ' Hence ' ( x ) ...
Side 51
... Hence we find dM - -y - x dy √ ( x2 + y2 ) ) y x Y y√ ( x2 + y2 ) * dN dy ̄ ̄ ( x2 + y2 ) $ ̄ ̄ dx To obtain the complete integral we will on this occasion employ directly the general form of solution ( 12 ) . We have Hence N- ― [ Mdx ...
... Hence we find dM - -y - x dy √ ( x2 + y2 ) ) y x Y y√ ( x2 + y2 ) * dN dy ̄ ̄ ( x2 + y2 ) $ ̄ ̄ dx To obtain the complete integral we will on this occasion employ directly the general form of solution ( 12 ) . We have Hence N- ― [ Mdx ...
Side 58
... Hence the general form of the integrating factor of the equa- tion is 1 x3y3 f ( +2 ) + 3/4 ) . 4. From the typical form of the integrating factor of the equation Mdx + Ndy = 0 , it follows that if we know two par- ticular integrating ...
... Hence the general form of the integrating factor of the equa- tion is 1 x3y3 f ( +2 ) + 3/4 ) . 4. From the typical form of the integrating factor of the equation Mdx + Ndy = 0 , it follows that if we know two par- ticular integrating ...
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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