Babyslapmafro
  • Babyslapmafro
Please help me solve the given differential equation by separation of variables. (4y+yx^2)dy=(2x+xy^2)dx
Mathematics
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SOLVED
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schrodinger
  • schrodinger
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Babyslapmafro
  • Babyslapmafro
\[(4y+yx^2)dy=(2x+xy^2)dx\]
anonymous
  • anonymous
ok this is a fun one :)
anonymous
  • anonymous
first you want to pull out the variables from each parenthesis, \[(4y + yx ^{2})dy = y(4 + x ^{2}) dy \] and \[(2x + xy ^{2}) dx = x(2 + y ^{2})\]

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anonymous
  • anonymous
Forgot the dx on 2nd part
anonymous
  • anonymous
Than the expression becomes \[y(4 + x^{2}) dy = x(2+y^{2}) dx\] divide so that X's are on right and Y's are on left
anonymous
  • anonymous
This gives you: \[\left( \frac{ y }{ 2 + y^{2} } \right) dy = \left( \frac{ x }{ 4+x^{2} } \right) dx\]
Babyslapmafro
  • Babyslapmafro
oh ok thank you, I believe I can go from here. should all solutions of separation of variable problems be set equal to y?
anonymous
  • anonymous
Well you want to get the y's with the dy and the x's with the dx
anonymous
  • anonymous
but most cases you are solving for a function that is of the form y(x)
anonymous
  • anonymous
y(x) = expression
Babyslapmafro
  • Babyslapmafro
right, but I'm talking about the final solution
Babyslapmafro
  • Babyslapmafro
right ok

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