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Although Euler's method is not very accurate compared to other numerical methods for solving ODE's, it is still powerful in the sense that it can deal with any equation which can be put in the form

$y^{(N)}(t)=f(t,y(t),...,y^{(N-1)}(t))$ (*)

However, can Euler's method deal with equations such as

$y=y'+\sin(y')$

Technically, this equation gives the system

$y'=x$ $x'=x/(1+\cos(x))$

which can be dealt with by Euler. So maybe this is a bad example.

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    I can approximate the solution, but beyond that no more... – 2017-01-20
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    @SimpleArt : that is of course what Euler's method does, it approximates solutions. I'm not asking for an exact solution... – 2017-01-20

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