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A Relation between two Ordinary Linear Differential Equations of the Second Order
Published online by Cambridge University Press: 31 October 2008
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1. Between the solutions of the equations
a relation can be established, provided the functional symbols f, ø are inverse to one another. For example, let f (x) = sin x, then ø(ξ)= arcsin ξ, and the two equations are
The process consists in obtaining from (1) the second order equation satisfied by yx = dy/dx, making a change of independent variable in (2), and comparing the resulting equations.
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- Copyright © Edinburgh Mathematical Society 1935
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