I try so not working.

DSolve[x Dt[x] == y [x] Dt[y], y[x], x]

I need to solve $x\ dx = y\ dy$.

  • 2
    $\begingroup$ DSolve[x Dt[x] == y[x] Dt[y[x]], y[x], x] $\endgroup$
    – zhk
    Jan 23, 2017 at 14:05

2 Answers 2

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]

enter image description here


The MMM answer is the simplest but remember how in textbooks they show how to solve an exact differential equation :

\*SubsuperscriptBox[\(∫\), \(a\), \(x\)]\(s \[DifferentialD]s\)\) == \!\(
\*SubsuperscriptBox[\(∫\), \(y[a]\), \(y[x]\)]\(t \[DifferentialD]t\)\), y[x]]

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