## Formulas and theorems in pure mathematics |

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Page 463

3167 To find when two

arbitrary constant, are equivalent. Rule. — Eliminate one of the variables. The

other will also disappear, and a relation between the arbitrary constants will

remain.

3167 To find when two

**solutions**of a differential equation, each involving anarbitrary constant, are equivalent. Rule. — Eliminate one of the variables. The

other will also disappear, and a relation between the arbitrary constants will

remain.

Page 491

George Shoobridge Carr. Eliminating a and b from (2), (3), and (4), we get the

differential equation y$sR%-w>* «□ the integral of which, and the singular

, p. 49.

George Shoobridge Carr. Eliminating a and b from (2), (3), and (4), we get the

differential equation y$sR%-w>* «□ the integral of which, and the singular

**solution**of (1), is -/(16y + 4a' + a!1) = x S(l + x*) + log {x+ •(l + <*)} + 0. [Boole, Sup., p. 49.

Page 507

+/»&, = ° (3), therefore either /„ = 0, ft= 0, leading to the singular

eliminating /„, f„, a, b„ — a„bx = 0, and therefore, by (3167), b = 0(a). Multiply

equations (3) by dx, dy respectively, and add, thus fada+fbdb = 0. Substitute 6 = tj

> (a) in ...

+/»&, = ° (3), therefore either /„ = 0, ft= 0, leading to the singular

**solution**; or,eliminating /„, f„, a, b„ — a„bx = 0, and therefore, by (3167), b = 0(a). Multiply

equations (3) by dx, dy respectively, and add, thus fada+fbdb = 0. Substitute 6 = tj

> (a) in ...

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### Contents

Introduction The C G S System of Units | 1 |

VHI Common and Hyperbolic Logarithms of | 7 |

QUANT1C8 1620 | 30 |

Copyright | |

108 other sections not shown

### Common terms and phrases

becomes Binomial Theorem bisect changes of sign chord circumscribing circle columns conic conjugate constant continued fraction convergent cosec cosine curve denoted determinant diameter divided eliminant ellipse equal equate coefficients expand factors figure formula function given circle given ratio Hence hyperbola imaginary roots infinite inscribed circle integer integral intersect inverse points limits logarithm method Multiply negative nine-point circle notation obtained orthogonally pair parabola parallel partial fractions perpendicular plane positive powers Proof Proof.—By Proof.—In Proof.—Let Proof.—The quantic quantities quotient radical axis radius respect result right angle rows Rule sides similar triangles Similarly sine singular solution solution squares substituting successive tangent Taylor's theorem theorem tion transformed triangle ABC unity vanishes variables zero