A Treatise on Differential Equations, Volum 1Macmillan, 1872 - 85 sider |
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Resultat 1-5 av 80
Side 29
... whence , eliminating do ' dx du dv du dv = 0 , dx dy dy dx . which shews , by Prop . I , that is a function of u . The second equation is then equivalent to f ( u ) = C , and this is resolvable by solution into equations of the form u ...
... whence , eliminating do ' dx du dv du dv = 0 , dx dy dy dx . which shews , by Prop . I , that is a function of u . The second equation is then equivalent to f ( u ) = C , and this is resolvable by solution into equations of the form u ...
Side 33
... whence dp = ndy n - sin y ndy φ = + c : n - sin y the integral in the second member is a known form . It will be remarked that the transformations employed in the above examples are not very obvious ones . They would scarcely be ...
... whence dp = ndy n - sin y ndy φ = + c : n - sin y the integral in the second member is a known form . It will be remarked that the transformations employed in the above examples are not very obvious ones . They would scarcely be ...
Side 34
... whence dividing by x √ ( 1 + v2 ) dx − xdv = 0 , from which result dx dv = 0 ; x √ ( 1 + v2 ) log x - log ( v + √ ( 1 + v2 ) } = c . y Replacing v by we have y y2 ) = C , loga - log ( + / + ) - c , for the complete primitive . As in ...
... whence dividing by x √ ( 1 + v2 ) dx − xdv = 0 , from which result dx dv = 0 ; x √ ( 1 + v2 ) log x - log ( v + √ ( 1 + v2 ) } = c . y Replacing v by we have y y2 ) = C , loga - log ( + / + ) - c , for the complete primitive . As in ...
Side 35
... whence on integrating log x + √ √ ( v ) + v ¥ ( v ) = C ............... ( 18 ) . It is obvious from the symmetry of the relation between x and y that we might equally employ the transformation = v X y and regard v and y as the new ...
... whence on integrating log x + √ √ ( v ) + v ¥ ( v ) = C ............... ( 18 ) . It is obvious from the symmetry of the relation between x and y that we might equally employ the transformation = v X y and regard v and y as the new ...
Side 37
... whence if a and ẞ be determined by the conditions aa + bB = c , a'a + b'ß = c ' , we shall have the homogeneous equation ( ax + by ' ) dx ' + ( a'x ' + b'y ' ) dy ' = 0 . Making then y = vx ' we find dx ' ( a ' + b'v ) dv + x ' a + ( b ...
... whence if a and ẞ be determined by the conditions aa + bB = c , a'a + b'ß = c ' , we shall have the homogeneous equation ( ax + by ' ) dx ' + ( a'x ' + b'y ' ) dy ' = 0 . Making then y = vx ' we find dx ' ( a ' + b'v ) dv + x ' a + ( b ...
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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