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- W30851888 abstract "This chapter focuses on solutions of constant coefficient linear equations. Linear constant coefficient ordinary differential equations have exponential solutions. The method of undetermined coefficients can be used to solve this type of equation after a polynomial has been factored. The chapter considers an n -th order linear equation y ( n ) + a n−1 y ( n-1 ) +…+ a 1 y'+ a 0 y = 0, where the { a i } are constants. A solution of the form y ( x ) = Ce λx is then searched, where C is an arbitrary constant. Substituting y ( x ) = Ce λx into y ( n ) + a n−1 y ( n-1 ) +…+ a 1 y'+ a 0 y = 0 yields e λ x [ λ n + a n −1 λ ( n-1 ) + …+ a 1 λ + a 0 ] = 0 hence, form y ( x ) = Ce λx is a solution of y ( n ) + a n−1 y ( n-1 ) +…+ a 1 y'+ a 0 y = 0 if λ is a root of the characteristic equation, defined by λ n + a n −1 λ ( n-1 ) +…+ a 1 λ + a 0 = 0." @default.
- W30851888 created "2016-06-24" @default.
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- W30851888 date "1992-01-01" @default.
- W30851888 modified "2023-09-26" @default.
- W30851888 title "Constant Coefficient Linear Equations" @default.
- W30851888 doi "https://doi.org/10.1016/b978-0-12-784391-9.50053-1" @default.
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