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- W1532362007 abstract "This chapter focuses on the version 1 of transformations of second-order linear ordinary differential equation (ODEs). The transformation is applicable to second-order linear ODEs y “ + a ( x ) y ' + b ( x ) y = 0. If the dependent and independent variables in y “ + a ( x ) y ' + b ( x ) y = 0 are changed by t = ∫exp (− ∫ a ( z ) dz ) dr , and w ( t ) = y ( x ), then y “ + a ( x ) y ' + b ( x ) y = 0 becomes d 2 w / dt 2 + b ( x ( t )) exp[−2 ∫ a ( z ) dz ] w = 0, two ordinary differential equations which have the same name normal form are said to be equivalent. The chapter also highlights that the invariant of the adjoint of equation y “ + a ( x ) y ' + b ( x ) y = 0 is equal to the invariant of y “ + a ( x ) y ' + b ( x ) y = 0. That is to say, invariants are preserved under the operation of taking the adjoint." @default.
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- W1532362007 date "1992-01-01" @default.
- W1532362007 modified "2023-09-27" @default.
- W1532362007 title "Transformations of Second Order Linear ODEs – 1" @default.
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- W1532362007 doi "https://doi.org/10.1016/b978-0-12-784391-9.50037-3" @default.
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