A Treatise on Differential Equations, Τόμος 1Macmillan, 1872 - 85 σελίδες |
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Αποτελέσματα 1 - 5 από τα 26.
Σελίδα 14
... regarding y as a function of x , we obtain directly , or by elimination of c1 , an equation of the first order of the form dy $ 1 ( X , Y , Z , C2 , C3 , ... C „ ) = 0 . dx ' Differentiating this equation with respect to a , and regarding ...
... regarding y as a function of x , we obtain directly , or by elimination of c1 , an equation of the first order of the form dy $ 1 ( X , Y , Z , C2 , C3 , ... C „ ) = 0 . dx ' Differentiating this equation with respect to a , and regarding ...
Σελίδα 50
... regarding y as constant , and adding , instead of an arbitrary constant , an arbitrary function of y , which must afterwards be determined by the condition that the differential coefficient of the sum with respect to y shall be equal to ...
... regarding y as constant , and adding , instead of an arbitrary constant , an arbitrary function of y , which must afterwards be determined by the condition that the differential coefficient of the sum with respect to y shall be equal to ...
Σελίδα 87
... regarding therein R as the independent and Q as the de- pendent variable , dQ ( 2c - R ) dR + 2Q = R , a linear equation of which the solution is Hence we have Q = R ― c + c ' ( R − 2c ) 2 . S = c ( R −c ) + cc ′ ( R − 2c ) 3 , and ...
... regarding therein R as the independent and Q as the de- pendent variable , dQ ( 2c - R ) dR + 2Q = R , a linear equation of which the solution is Hence we have Q = R ― c + c ' ( R − 2c ) 2 . S = c ( R −c ) + cc ′ ( R − 2c ) 3 , and ...
Σελίδα 122
... regarding p as a new variable , we form a differential equation between p and the variable which does not enter into the original equation , and integrate the equation thus formed , the elimina- tion of p between the resulting integral ...
... regarding p as a new variable , we form a differential equation between p and the variable which does not enter into the original equation , and integrate the equation thus formed , the elimina- tion of p between the resulting integral ...
Σελίδα 128
... regarding y as the independent variable , ť dx + p + y dy dy dp2ap dp dy dx whence , replacing - by and reducing , 2 y - 2ap3 1 + p2 dy P dy Ρ + dp 1 + p therefore on integration y = 1 √ ( 1 + p3 ) - · [ C + ap √ ( 1 + p3 ) − a log ...
... regarding y as the independent variable , ť dx + p + y dy dy dp2ap dp dy dx whence , replacing - by and reducing , 2 y - 2ap3 1 + p2 dy P dy Ρ + dp 1 + p therefore on integration y = 1 √ ( 1 + p3 ) - · [ C + ap √ ( 1 + p3 ) − a log ...
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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