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Can you help me to find all solutions of differential equation $y'^2-(x+y)y'+xy=0$?

I wrote this equation as product of explicit equations:

$$(y'-x)(y'-y)=0$$

Then I found zeroes: $y'-x=0 \Longrightarrow y'=x \Longrightarrow y=\frac{x^2}2+C_1$

$y'=0$ I don't know what to do here. Maybe to solve as equation 'without $x$'? Am I doing this right?

  • 0
    see this http://www.wolframalpha.com/input/?i=y%27^2-%28x%2By%29y%27%2Bxy%3D02011-12-08
  • 0
    copy whole part ,not only blue2011-12-08
  • 0
    so, it's good what I did? how did it get y=C1e^x?2011-12-08
  • 0
    see solution i have posted2011-12-08

3 Answers 3