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Every second-order linear ODE with three regular singular points can be transformed into this equation.

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## Some Related Sentences

Every and second-order

For example,

__second-order__arithmetic**can**express the principle "__Every__countable vector space has a basis " but it cannot express the principle "__Every__vector space has a basis ".
Many principles that imply the axiom of choice in their general form ( such as "

__Every__vector space has a basis ") become provable in weak subsystems of__second-order__arithmetic when they are restricted**.**
* ( Soundness )

__Every__provable__second-order__sentence is universally valid, i**.**e., true in all domains under standard semantics**.**
* ( Completeness )

__Every__universally valid__second-order__formula, under standard semantics, is provable**.**__Every__

__second-order__

**linear**

**ODE**on the extended complex plane

**with**at most four

**regular**

**singular**

**points**, such as the Lamé

**equation**or the hypergeometric differential

**equation**,

**can**

**be**

**transformed**

**into**

**this**

**equation**by a change of variable

**.**

Every and linear

__Every__module over a division ring has a basis ;

__linear__maps between finite-dimensional modules over a division ring

**can**

**be**described by matrices, and the Gaussian elimination algorithm remains applicable

**.**

__Every__time a diode switches from on to off or vice versa, the configuration of the

__linear__network changes

**.**

__Every__vector v in determines a

__linear__map from R to taking 1 to v, which

**can**

**be**thought of as a Lie algebra homomorphism

**.**

__Every__smooth ( or differentiable ) map φ: M → N between smooth ( or differentiable ) manifolds induces natural

__linear__maps between the corresponding tangent spaces:

*

__Every____linear__combination of its components Y = a < sub > 1 </ sub > X < sub > 1 </ sub > + … + a < sub > k </ sub > X < sub > k </ sub > is normally distributed**.**__Every__continuous function in the function space

**can**

**be**represented as a

__linear__combination of basis functions, just as every vector in a vector space

**can**

**be**represented as a

__linear__combination of basis vectors

**.**

__Every__sedenion is a real

__linear__combination of the unit sedenions 1, < var > e </ var >< sub > 1 </ sub >, < var > e </ var >< sub > 2 </ sub >, < var > e </ var >< sub > 3 </ sub >, ..., and < var > e </ var >< sub > 15 </ sub >,

__Every__physical quantity has a Hermitian

__linear__operator associated to it, and the states where the value of

**this**physical quantity is definite are the eigenstates of

**this**

__linear__operator

**.**

__Every__nontrivial proper rotation in 3 dimensions fixes a unique 1-dimensional

__linear__subspace of R < sup > 3 </ sup > which is called the axis of rotation (

**this**is Euler's rotation theorem ).

__Every__finite-dimensional normed space is reflexive, simply because in

**this**case, the space, its dual and bidual all have the same

__linear__dimension, hence the

__linear__injection J from the definition is bijective, by the rank-nullity theorem

**.**

__Every__finite-dimensional Hausdorff topological vector space is reflexive, because J is bijective by

__linear__algebra, and because there is a unique Hausdorff vector space topology on a finite dimensional vector space

**.**

__Every__bounded

__linear__transformation from a normed vector space to a complete, normed vector space

**can**

**be**uniquely extended to a bounded

__linear__transformation from the completion of to

**.**

__Every__vector a in

**three**dimensions is a

__linear__combination of the standard basis vectors i, j, and k

**.**

__Every__lattice in

**can**

**be**generated from a basis for the vector space by forming all

__linear__combinations

**with**integer coefficients

**.**

__Every__

__linear__program has a dual problem

**with**the same optimal solution, but the variables in the dual problem correspond to constraints in the primal problem and vice versa

**.**

Every and with

__Every__detail in his interpretation has been beautifully thought out, and of these I would especially cite the delicious laendler touch the pianist brings to the fifth variation ( an obvious indication that he is playing

__with__Viennese musicians ), and the gossamer shading throughout

**.**

__Every__Wednesday night through Oct. 11 there will

**be**an elaborate colored fountain display,

__with__229 nozzles throwing jets of water up to 130 feet

**.**

** Tukey's lemma:

__Every__non-empty collection of finite character has a maximal element__with__respect to inclusion**.**__Every__unit of length has a corresponding unit of area, namely the area of a square

__with__the given side length

**.**

* Revised Code of Washington 9

**.**12**.**010: "__Every__person who brings on his or her own behalf, or instigates, incites, or encourages another to bring, any false suit at law or in equity in any court of**this**state,__with__intent thereby to distress or harass a defendant in the suit, or who serves or sends any paper or document purporting to**be**or resembling a judicial process, that is not in fact a judicial process, is guilty of a misdemeanor ; and in case the person offending is an attorney, he or she may, in addition thereto**be**disbarred from practicing law within**this**state**.**__Every__Boolean algebra ( A, ∧, ∨) gives rise to a ring ( A, +, ·) by defining a + b := ( a ∧ ¬ b ) ∨ ( b ∧ ¬ a ) = ( a ∨ b ) ∧ ¬( a ∧ b ) (

**this**operation is called symmetric difference in the case of sets and XOR in the case of logic ) and a · b := a ∧ b

**.**The zero element of

**this**ring coincides

__with__the 0 of the Boolean algebra ; the multiplicative identity element of the ring is the 1 of the Boolean algebra

**.**

__Every__Hilbert space X is a Banach space because, by definition, a Hilbert space is complete

__with__respect to the norm associated

__with__its inner product, where a norm and an inner product are said to

**be**associated if for all x ∈ X

**.**

*

__Every__quadratic Bézier curve is also a cubic Bézier curve, and more generally, every degree n Bézier curve is also a degree m curve for any m > n**.**In detail, a degree n curve__with__control**points**P < sub > 0 </ sub >, …, P < sub > n </ sub > is equivalent ( including the parametrization ) to the degree n + 1 curve__with__control**points**P '< sub > 0 </ sub >, …, P '< sub > n + 1 </ sub >, where**.**
*

__Every__unital real Banach algebra__with__no zero divisors, and in which every principal ideal is closed, is isomorphic to the reals, the complexes, or the quaternions**.**
*

__Every__commutative real unital Noetherian Banach algebra__with__no zero divisors is isomorphic to the real or complex numbers**.**
Jimmy Hatlo's They'll Do It

__Every__Time was often displayed in a two-panel format__with__the first panel showing some deceptive, pretentious, unwitting or scheming human behavior and the second panel revealing the truth of the situation**.**__Every__year, the European Joint Conferences on Theory and Practice of Software ( ETAPS ) sponsors the International Conference on Compiler Construction ( CC ),

__with__papers from both the academic and industrial sectors

**.**

According to

__Every__, one example may**be**" the myth of St**.**George " and other stories about saints battling dragons, which were " modelled no doubt in many cases on older representations of the creator and preserver of the world in combat__with__chaos ".
*

__Every__**three**years since Earnhardt's death, someone associated__with__Earnhardt has won the Daytona 500 ( his son Dale Earnhardt, Jr**.**in 2004, Earnhardt's replacement Cup driver Kevin Harvick in 2007, and Earnhardt Ganassi's Jamie McMurray in 2010**.**
In Norse mythology, Draupnir ( Old Norse " the dripper ") is a gold ring possessed by the god Odin

__with__the ability to multiply itself:__Every__ninth night eight new rings ' drip ' from Draupnir, each one of the same size and weight as the original**.**__Every__system must have a class designated as " root ",

__with__one of its creation procedures designated as " root procedure ".

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