Examples of the Processes of the Differential and Integral CalculusJ and J. J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 1-5 із 19
Сторінка x
... Singular Solutions of Differential Equations ....... 400 IX . Quadrature of Areas and Surfaces , Rectification of Curves , and Cubature of Solids 412 X. Geometrical Problems Involving the Solution of Differential Equations 440 XI ...
... Singular Solutions of Differential Equations ....... 400 IX . Quadrature of Areas and Surfaces , Rectification of Curves , and Cubature of Solids 412 X. Geometrical Problems Involving the Solution of Differential Equations 440 XI ...
Сторінка 331
... singular solution is found by eliminating p between the given equation and x + ƒ ' ( p ) = 0 . This equation is ... singular solution is x2 + y2 = n2 . ( 11 ) Let y = px + p- p2 . ( 12 ) Let The general integral is the singular solution ...
... singular solution is found by eliminating p between the given equation and x + ƒ ' ( p ) = 0 . This equation is ... singular solution is x2 + y2 = n2 . ( 11 ) Let y = px + p- p2 . ( 12 ) Let The general integral is the singular solution ...
Сторінка 332
... general integral is a C ( c - 2 c2 ) . 4 The singular solution is 4ay2 + ( 2x − b ) = 0 . ( 15 ) Let axy dy d x 2 dy + ( b x2 - ay2 – ab ) - - - bxy = = 0 . dx On multiplying by 4xy , and taking a2 and y ' as the new variables , the ...
... general integral is a C ( c - 2 c2 ) . 4 The singular solution is 4ay2 + ( 2x − b ) = 0 . ( 15 ) Let axy dy d x 2 dy + ( b x2 - ay2 – ab ) - - - bxy = = 0 . dx On multiplying by 4xy , and taking a2 and y ' as the new variables , the ...
Сторінка 334
... singular solution y = Cx . Sometimes an equation may be considered homogeneous by reckoning a as of one dimension , y of n dimensions , and d2y consequently of ( n - 1 ) dimensions , and of ( n - 2 ) dy dx dx2 x " u , p = x - 1t ...
... singular solution y = Cx . Sometimes an equation may be considered homogeneous by reckoning a as of one dimension , y of n dimensions , and d2y consequently of ( n - 1 ) dimensions , and of ( n - 2 ) dy dx dx2 x " u , p = x - 1t ...
Сторінка 335
... singular solution . If & be reckoned of o dimensions so that dy d'y y , dx ' da2 are of the same dimensions , a homogeneous equation may be integrated by assuming p = uy , q = vy ; whence as dy uyda and udy + ydu = vydx , = dy y = udx ...
... singular solution . If & be reckoned of o dimensions so that dy d'y y , dx ' da2 are of the same dimensions , a homogeneous equation may be integrated by assuming p = uy , q = vy ; whence as dy uyda and udy + ydu = vydx , = dy y = udx ...
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a² b2 a²x² angle arbitrary constant asymptote axis becomes C₁ c²x² Cambridge circle co-ordinates condition curvature curve cycloid cylinder determine differential coefficients differential equation dx dx dx dy dx dx² dy dx dy dy dy dy dz eliminate ellipse equal Euler find the value formula function Geometry gives Hence hypocycloid infinite Integrating with respect intersection John Bernoulli Let the equation lines of curvature locus logarithmic logarithmic spiral maximum minimum Multiply negative origin parabola perpendicular radius radius of curvature singular solution spiral Substituting subtangent surface tangent plane theorem tractory triangle vanish whence x²)³