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Examples (1)The set of the solutions to the differential equation Py dz2-=0 (*) is a vector space V under the rules of and.for functions, Example ll of the last lecture. Then this vector space is spaned by e2 and e-.If y is a solution of (*)then there are constants(scalars)c1,c2 ER such that y(x)=cle=+ce-=. 4口+++左+4生+定QCExamples (1) The set of the solutions to the differential equation d 2y dx2 − y = 0 (∗) is a vector space V under the rules of + and • for functions, Example II of the last lecture. Then this vector space is spaned by e x and e −x . If y is a solution of (∗), then there are constants (scalars) c1, c2 ∈ R such that y(x) = c1e x + c2e −x
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