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Answer by Lutz Lehmann for Must any nth order homogeneous ODE have n solutions?
To the end of the question, you have worked your way towards a more realistic picture, the initial premise is formulated unfortunately, since every differential equation has an infinity of...
View ArticleAnswer by Qiaochu Yuan for Must any nth order homogeneous ODE have n solutions?
Let me restrict attention to the linear case. Then the space of solutions is a vector space, and one can ask what its dimension is. The answer, for an $n^{th}$ order homogeneous linear ODE (with...
View ArticleMust any nth order homogeneous ODE have n solutions?
I am quite confused about ordinary differential equations and the number of solutions they have. In particular, it seems that an nth order homogeneous differential equation has n solutions, not more or...
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