I know that we take characteristic polynomial of forms like $\lambda^2 - \lambda - 2$ to find out the solution of ordinary differential equation of the form $e^{\lambda x}$ - conjugate ones can be slightly modified. The question is, there are other forms of solution, right? So, why do people just use superposition of natural exponentiation forms when other solutions are available? Or am I mistaken?
Properties of ordinary differential equations - solution
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ordinary-differential-equations
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1There are no more. – 2012-12-25