Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 6-10 із 76
Сторінка 44
... Multiplying the former by and adding , ( 6 ) d2y dx + r2y = 0 . Eliminate m and a from the equation y2 = m ( a2 − x2 ) ; - dey 2 ( dy the result is xy + x dx2 dx - dy y = 0 . da ( 7 ) Eliminate c from the equation a - y - ce ̄ ̄ ...
... Multiplying the former by and adding , ( 6 ) d2y dx + r2y = 0 . Eliminate m and a from the equation y2 = m ( a2 − x2 ) ; - dey 2 ( dy the result is xy + x dx2 dx - dy y = 0 . da ( 7 ) Eliminate c from the equation a - y - ce ̄ ̄ ...
Сторінка 45
... Multiply numerator and denominator by e , then y = y + 1 whence € 2 " = y and differentiating , - dy dx € 2 + 1 1 9 = - and 2x = 1 - y2 . y + 1 log y 1 ( 12 ) Eliminate the power from the equation y ELIMINATION OF CONSTANTS AND ...
... Multiply numerator and denominator by e , then y = y + 1 whence € 2 " = y and differentiating , - dy dx € 2 + 1 1 9 = - and 2x = 1 - y2 . y + 1 log y 1 ( 12 ) Eliminate the power from the equation y ELIMINATION OF CONSTANTS AND ...
Сторінка 47
... Multiply ( 1 ) by x , ( 2 ) by y and add , dz dz 20 + y = nz . dx dy This is the differential equation to all homogeneous func- tions of n dimensions . It is to be observed that the two arbitrary functions are really equivalent to one ...
... Multiply ( 1 ) by x , ( 2 ) by y and add , dz dz 20 + y = nz . dx dy This is the differential equation to all homogeneous func- tions of n dimensions . It is to be observed that the two arbitrary functions are really equivalent to one ...
Сторінка 49
... Multiplying by dz 2 d2z dz dy - 2 " dx dy dz dx " = f dy 3 and subtracting , dz dz d2 dx2 dx dy dx dy This is the general equation to 2 + dx ( da ) * 2 ď2 z = 0 . dy surfaces generated by the motion of a line which constantly rests on ...
... Multiplying by dz 2 d2z dz dy - 2 " dx dy dz dx " = f dy 3 and subtracting , dz dz d2 dx2 dx dy dx dy This is the general equation to 2 + dx ( da ) * 2 ď2 z = 0 . dy surfaces generated by the motion of a line which constantly rests on ...
Сторінка 50
... Multiplying by a , b and subtracting , we obtain as the result of the elimination of the functions 2 ' dz a2 - - b2 dx2 Jd2 ≈ dy - 1 \ dy ( d ) " } = 0 . ( 23 ) Eliminate the arbitrary functions from ( 1 ) x ƒ ( a ) + y $ ( a ) + ...
... Multiplying by a , b and subtracting , we obtain as the result of the elimination of the functions 2 ' dz a2 - - b2 dx2 Jd2 ≈ dy - 1 \ dy ( d ) " } = 0 . ( 23 ) Eliminate the arbitrary functions from ( 1 ) x ƒ ( a ) + y $ ( a ) + ...
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Загальні терміни та фрази
a² b2 a²x² angle arbitrary constant asymptote becomes C₁ c²x² Cambridge circle co-ordinates condition Crelle's Journal curvature curve cycloid determine differential coefficients differential equation dx dx dx dy dx dy dx dx² dy dx dy dy dy dy dz dz dz eliminate ellipse equal Euler factor formula fraction function Geometry gives Hence hypocycloid infinite intersection John Bernoulli Let the equation lines of curvature locus logarithmic logarithmic spiral Multiply negative origin parabola perpendicular plane of reference radius SECT singular solution spiral Substituting subtangent surface tangent plane theorem triangle vanish whence x²)³