- #1
Ackbach
Gold Member
MHB
- 4,155
- 91
Here is this week's POTW:
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Find a one-parameter family of solutions of
$$(2x-y+1)\, dx+(x+y) \, dy=0.$$
Extra Credit: Generalize to
$$(ax+by+c) \, dx+(fx+gy+h) \, dy=0,$$
where $a,b,c,f,g,h$ are constants, and $\tfrac{b}{a}\not=\tfrac{g}{f}$.
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Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to http://www.mathhelpboards.com/forms.php?do=form&fid=2!
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Find a one-parameter family of solutions of
$$(2x-y+1)\, dx+(x+y) \, dy=0.$$
Extra Credit: Generalize to
$$(ax+by+c) \, dx+(fx+gy+h) \, dy=0,$$
where $a,b,c,f,g,h$ are constants, and $\tfrac{b}{a}\not=\tfrac{g}{f}$.
-----
Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to http://www.mathhelpboards.com/forms.php?do=form&fid=2!