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...Second order linear differential equations a equation has the form dy p x dx q r y g where and are continuous functions we saw in section that of this type arise study motion spring additional topics applications will further pursue application as well to electric circuits case for all such equa tions called homogeneous thus is if some nonhomogeneous discussed two basic facts enable us solve rst these says know solutions an then combination c also solution theorem both tion any constants function proof since have therefore using rules differentiation other fact need given by following which proved more advanced courses it general linearly independent means neither nor constant multiple instance f t dependent but ex xex never arbitrary very useful because particular inde pendent every not easy discover always possible do so coefcient ay cy b s hard think likely candidates state verbally looking times its derivative plus another third equal exponential erx prop rx erty itself re furtherm...