Theory of Higher-Order Linear Diﬀerential Equations 6.1 Basic Theory A linear diﬀerential equation of order n has the form a n(x)y(n)(x)+a n−1(x)y(n−1)(x)+···+a 0(x)y(x) = b(x), (6.1.1)
The theorem is valid for higher order equations: the general solution of the non-homogeneous equation is y = y h + y p, where y h is the general solution of the homogeneous equation and y
Linear Di erential Equations of Higher Order General Solution of homogeneous linear di erential equations Existence and Uniqueness of the Solution to an IVP Theorem For the given linear di
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260 Higher-Order Linear Equations: Deﬁnitions and Some Basic Theory A second-order differential equation is said to be linear if and only if it can be written as a 0 d2y dx2 + a 1 dy dx
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