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Differential Equations And Linear Algebra ebook download Sturgeon Tales In mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form + ′ + ″ + ⋯ + () + =,where (), ..., () and () are arbitrary differentiable functions that do not need to be linear, and ′, …, are the successive derivatives of an unknown function y of the variable x. is also sometimes called "homogeneous." In general, an th-order ODE has linearly independent solutions. Furthermore, any linear combination of linearly independent functions solutions is also a solution.. Simple theories exist for first-order (integrating factor) and second-order (Sturm-Liouville theory) ordinary differential equations, and arbitrary ODEs with linear constant coefficients can ... 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