I try so not working.
DSolve[x Dt[x] == y [x] Dt[y], y[x], x] I need to solve $x\ dx = y\ dy$.
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2 Answers
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DSolve[x Dt[x] == y[x] Dt[y], y[x], x] DSolve::dvnoarg: The function y appears with no arguments.
The warning says that the function y in some place is without any arguments, i.e., Dt[y]. Thus you need to change Dt[y] to this Dt[y[x]]
DSolve[x Dt[x] == y[x] Dt[y[x]], y[x], x] 
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The MMM answer is the simplest but remember how in textbooks they show how to solve an exact differential equation :
Solve[\!\( \*SubsuperscriptBox[\(∫\), \(a\), \(x\)]\(s \[DifferentialD]s\)\) == \!\( \*SubsuperscriptBox[\(∫\), \(y[a]\), \(y[x]\)]\(t \[DifferentialD]t\)\), y[x]] 
DSolve[x Dt[x] == y[x] Dt[y[x]], y[x], x]$\endgroup$