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I have differential equation $x\cdot\sqrt{4+y^2}\,dx + y\cdot\sqrt{1+x^2}\,dy = 0$, which is simple to solve on paper, but I have problem solving it with Maple (I use 10th, tried on 14th also). When applying dsolve it complains that it is not ODE. Any suggestions? Thank you in advance

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Did you try dividing through by $dx$? This will eliminate $dx$ and replace $dy$ with $y'$. – Yuval Filmus Mar 8 '11 at 9:12
I believe the command you are looking for is "dsolve(x*sqrt(4+y(x)^2)+y(x)*sqrt(1+x^2)*diff(y(x),x), y(x))" – Fabian Mar 8 '11 at 9:17
@Fabian Could post as an answer. Because it is perfectly working solution. Thank you. – Kukmedis Mar 8 '11 at 9:25
up vote 3 down vote accepted

The command you are looking for is

dsolve(x*sqrt(4+y(x)^2)+y(x)*sqrt(1+x^2)*diff(y(x),x), y(x)).

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It looks better if you include code in backticks (`code`): dsolve(x*sqrt(4+y(x)^2)+y(x)*sqrt(1+x^2)*diff(y(x),x), y(x)) – t.b. Mar 8 '11 at 9:38
Thank you...... – Fabian Mar 8 '11 at 9:42

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