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I would like to resolve this differential equation:

$xx'-x=f(t)$

any suggestions (or any online texts on similar differential equation) please? Thanks.

2 Answers 2

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This is an 'Abel equation of the second kind in the canonical form'.

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    Thanks! And is this Abel equation? $xx'-g(t)x=f(t)$2012-07-07
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    @Mark: More exactly this is a ['special case of the Abel differential equation of the second kind'](http://eqworld.ipmnet.ru/en/solutions/ode/ode0125.pdf) while the ['Abel differential equation of the second kind'](http://eqworld.ipmnet.ru/en/solutions/ode/ode0126.pdf) incorporates a x^2 term.2012-07-07
  • 0
    Although the recognition of EqWorld is quite well, it still behaves outdated about Abel differential equation of the second kind, since the article http://www.hindawi.com/journals/ijmms/2011/387429/#sec2 has been issued.2012-07-07
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Although the recognition of EqWorld is quite well, it still behaves outdated about Abel equation of the second kind.

The following information is really updated indeed:

$xx'-x=f(t)$ itself belongs to an Abel equation of the second kind in the canonical form.

Please follow the method in https://arxiv.org/ftp/arxiv/papers/1503/1503.05929.pdf