With no explanation, label text_A→text_B with either "not_related" or "related".
text_A: Neal Schon was born on the 28th.
text_B: A singular solution ys -LRB- x -RRB- of an ordinary differential equation is a solution that is singular or one for which the initial value problem -LRB- also called the Cauchy problem by some authors -RRB- fails to have a unique solution at some point on the solution .. ordinary. ordinary differential equation. differential equation. differential equation. singular. Mathematical singularity. initial value problem. initial value problem. The set on which a solution is singular may be as small as a single point or as large as the full real line .. singular. Mathematical singularity. Solutions which are singular in the sense that the initial value problem fails to have a unique solution need not be singular functions .. singular. Mathematical singularity. initial value problem. initial value problem. singular functions. Mathematical singularity. In some cases , the term singular solution is used to mean a solution at which there is a failure of uniqueness to the initial value problem at every point on the curve .. singular. Mathematical singularity. initial value problem. initial value problem. A singular solution in this stronger sense is often given as tangent to every solution from a family of solutions .. singular. Mathematical singularity. tangent. tangent. By tangent we mean that there is a point x where ys -LRB- x -RRB- = yc -LRB- x -RRB- and y 's -LRB- x -RRB- = y' c -LRB- x -RRB- where yc is a solution in a family of solutions parameterized by c .. tangent. tangent. This means that the singular solution is the envelope of the family of solutions .. singular. Mathematical singularity. envelope. envelope ( mathematics ). Usually , singular solutions appear in differential equations when there is a need to divide in a term that might be equal to zero .. singular. Mathematical singularity. zero. 0 ( number ). Therefore , when one is solving a differential equation and using division one must check what happens if the term is equal to zero , and whether it leads to a singular solution .. differential equation. differential equation. singular. Mathematical singularity. zero. 0 ( number ). The Picard -- Lindelof theorem , which gives sufficient conditions for unique solutions to exist , can be used to rule out the existence of singular solutions .. singular. Mathematical singularity. Other theorems , such as the Peano existence theorem , give sufficient conditions for solutions to exist without necessarily being unique , which can allow for the existence of singular solutions .. singular. Mathematical singularity. Peano existence theorem. Peano existence theorem
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