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It is shown that the modified Emden equation q̈+α(t)q̇+qn=0 possesses first integrals for functions α(t) other than kt−1. The function α(t) is obtained explicitly in the case n=3 and parametrically for other n(≠2). The case n=2 is seen to be particularly difficult to solve.
P. G. L. Leach (Tue,) studied this question.
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