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Math Help - Need help with this initial-value problem

  1. #1
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    Question Need help with this initial-value problem

    Find the solution of the given initial value problem in explicit form.

    y' = x(x+1) / 4y, y(0) = -1 /√2

    According to my textbook, the correct answer is y= -√((x+1)/2)

    Here is what I am doing and hopefully someone can tell me where I'm going wrong. I can see that it is separable, so I separated it and integrating both sides I got y^4=1/4x^4 + 1/2x + C. Solving for C I got 1/4, however I am not sure that any of this is correct so far. Anyways, I know I'll never get the right answer unless I get the correct implicit solution and the correct value of C, so help me out with those if what I have written is incorrect!
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  2. #2
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    Quote Originally Posted by steph3824 View Post
    Find the solution of the given initial value problem in explicit form.

    y' = x(x+1) / 4y, y(0) = -1 /√2

    According to my textbook, the correct answer is y= -√((x+1)/2)

    Here is what I am doing and hopefully someone can tell me where I'm going wrong. I can see that it is separable, so I separated it and integrating both sides I got y^4=1/4x^4 + 1/2x + C. Solving for C I got 1/4, however I am not sure that any of this is correct so far. Anyways, I know I'll never get the right answer unless I get the correct implicit solution and the correct value of C, so help me out with those if what I have written is incorrect!
    Okay so you have (It is correct) Just keep going

    y^4=\frac{1}{4}x^4+\frac{1}{2}x^2+\frac{1}{4}

    Now lets simplify the right hand side a bit

    y^4=\frac{1}{4}(x^4+2x^2+1)=\frac{1}{4}(x^2+1)^2

    Now take the 4th roots and simplify.(don't forget the plus or minus) The intial conditions which root you need to take to satisfy the equaiton.

    I hope this helps
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  3. #3
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    That was definitely helpful...I was able to get to the correct answer after you showed the best way to simplify it, thanks!!
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