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System of non-linear differential equations

Posted 6 years ago
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$${x(t)^2 y''(t)+2 x(t) x'(t) y'(t)-9, 81 (x(t) cos(y(t))-sin(y(t))) = 0, x''(t)-x'(t) y'(t)^2+x(t)-9, 81 sin(y(t)) = 0}$$

i've tried to input this on wolfram alpha but can't solve, could anyone help me how to have it solved? P.S.

it's a system of equations which comes from a mechanical problem that i shouldn't be able to solve for my math knowledges but i'd like to view solution to understand how it works at least

I cannot tell whether the comma in "9.81" is a punctuation comma -- which would be a syntax error in your expression -- or whether, instead, it's supposed to be a decimal point, which by default you'd need to enter as 9.81 in Mathematica. I suspect the latter, since I suspect you're referring to average gravitational acceleration on surface of Earth,

Offhand, the differential equations as given look quite nasty, and I would not expect an exact symbolic solution -- even after you replaced the approximate number 9.81 by the exact rational 981/100.

So you should try to do a numerical solution, and for that you'll need some initial conditions.

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