anonymous
  • anonymous
This is one requires substitution, but i don't what i am doing wrong...
Differential Equations
schrodinger
  • schrodinger
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anonymous
  • anonymous
\[yy \prime+x=(x ^{2}+y ^{2})^{1/2}\]
anonymous
  • anonymous
i tried subsitituting \[u = x ^{2}+y ^{2}\]
anonymous
  • anonymous
@UnkleRhaukus

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UnkleRhaukus
  • UnkleRhaukus
why did you think of that substitution?
anonymous
  • anonymous
because it would simplify the right side tremendously...but not too sure.
UnkleRhaukus
  • UnkleRhaukus
but what would y' become?
anonymous
  • anonymous
\[(1/y)((du/dx)-x)\]
anonymous
  • anonymous
but when i substitute it get very messy.
UnkleRhaukus
  • UnkleRhaukus
substitute and try that simplification again
UnkleRhaukus
  • UnkleRhaukus
the mess should work it self out
anonymous
  • anonymous
ok thanks!
UnkleRhaukus
  • UnkleRhaukus
tell me what you get,
anonymous
  • anonymous
this is what i have so far...
anonymous
  • anonymous
\[1/y \left( (u-x ^{2})^{1/2} - x(u-x ^{2})^{1/2} \right) + x = u ^{1/2}\]
anonymous
  • anonymous
oh wait ....i forgot about that y
anonymous
  • anonymous
got it!
anonymous
  • anonymous
i get c.
anonymous
  • anonymous
thank you very much!
UnkleRhaukus
  • UnkleRhaukus
\[u'=√u\]

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