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Math Help - Sample ODE question

  1. #1
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    Sample ODE question

    How do solve \displaystyle\frac{dy}{dx}+y^2+2x=0 ?
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  2. #2
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    Quote Originally Posted by math2009 View Post
    How do solve \displaystyle\frac{dy}{dx}+y^2+2x=0 ?
    Why? Click on this: solve dy/dx + y^2 + 2x = 0 - Wolfram|Alpha
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    Please check my solution, I doubt there are something wrongs in Sample ODE question-math_q111en.pdf
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    Quote Originally Posted by math2009 View Post
    Please check my solution, I doubt there are something wrongs in Click image for larger version. 

Name:	MATH_Q111EN.pdf 
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    Your method is wrong and your solution is wrong (did you even bother to check the solution by substituting it into the original DE?)

    Although y = \frac{1}{2x + a} satisfies \frac{dy}{dx} + 2y^2 = 0, it is also required to satisfy \frac{dy}{dx} + 4 = 0 and it doesn't. Similarly, the other part of your 'solution' has to satisfy both \frac{dy}{dx} + 2y^2 = 0 and \frac{dy}{dx} + 4 = 0 ....
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    I also thought so before.
    If a,b are variable but not constants, how about ?
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  6. #6
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    Quote Originally Posted by math2009 View Post
    I also thought so before.
    If a,b are variable but not constants, how about ?
    That wouldn't seem a very useful 'solution' to me.
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    My opinion is : \begin{bmatrix}x \\y \end{bmatrix} \rightarrow \begin{bmatrix}x(a,b) \\ y(a,b) \end{bmatrix}

    If equation#1 's solution is E_1 and equation#2 's is E_2 , then E_1\cap E_2 must fit both equations, is it right ?
    And F(x, a, b) = 0 , it may simply solution
    Last edited by math2009; July 6th 2010 at 11:49 PM.
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  8. #8
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    Quote Originally Posted by math2009 View Post
    My opinion is : \begin{bmatrix}x \\y \end{bmatrix} \rightarrow \begin{bmatrix}x(a,b) \\ y(a,b) \end{bmatrix}

    If equation#1 's solution is E_1 and equation#2 's is E_2 , then E_1\cap E_2 must fit both equations, is it right ?
    And F(x, a, b) = 0 , it may simply solution
    You are wrong and I have told you why. I am not spending any more time discussing this.
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  9. #9
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    mr fantastic , at first , thank you for discussion
    please ignore this post.

    There are two cases in this issue.

    Case #1(constant) , as above mention, that's wrong.

    Case #2(variables) , is there any proof ?
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