How to solve equations like this one?
$\dfrac{dx}{dt} = \sin(x) +\tan(x) + x^2$
I have tried a few substitutions but none of them seems to work because of the $x^2$ term.
2026-03-25 11:04:48.1774436688
$\frac{dx}{dt} = \sin(x) +\tan(x) + x^2.$ How do I get $x$ as a function of $t$?
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I doubt it has a closed solution.
If you want a numerical solution, you can rearrange it as $$\int \frac{dx}{\sin x+\tan x+x^2} = t + C$$ and feed the integral into your calculator.
There are some constant solutions, where $\sin x + \tan x+x^2=0$. They are just above $(n+1/2)\pi$, where $\tan x$ is negative and large enough to counter $x^2$.