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Math Help - Solve dy/dx=-1-x+xy(x)+y^2 (x)

  1. #1
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    Solve dy/dx=-1-x+xy(x)+y^2 (x)

    pls help solve
    dy/dx=-1-x+xy(x)+y^2 (x)
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  2. #2
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    Quote Originally Posted by snehalkhair View Post
    pls help solve
    dy/dx=-1-x+xy(x)+y^2 (x)
    This is a Ricatti equation. I suggest you review the appropriate theory.
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  3. #3
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    I will say that one solution to this ODE is y = 1.
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  4. #4
    Senior Member bugatti79's Avatar
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    Quote Originally Posted by Danny View Post
    I will say that one solution to this ODE is y = 1.
    Is that because upon substitution dy/dx =0 implies y must be a constant? But how 1?
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  5. #5
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    Quote Originally Posted by bugatti79 View Post
    Is that because upon substitution dy/dx =0 implies y must be a constant? But how 1?
    y = 1 satisfies the original ODE. Just plug it in and see for yourself. I believe Danny mentioned this because if you have a particular solution for a Ricatti equation, you can get the general equation by using the appropriate method, as mr f suggested the OP'er look up.
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  6. #6
    Senior Member bugatti79's Avatar
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    Quote Originally Posted by Ackbeet View Post
    y = 1 satisfies the original ODE. Just plug it in and see for yourself. I believe Danny mentioned this because if you have a particular solution for a Ricatti equation, you can get the general equation by using the appropriate method, as mr f suggested the OP'er look up.
    Thats what I did..i think. just subbing in 1 for y in the rhs of ODE we get dy/dx=0.
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  7. #7
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    Quote Originally Posted by bugatti79 View Post
    Thats what I did..i think. just subbing in 1 for y in the rhs of ODE we get dy/dx=0.
    Yes, that's the point. Since y= 1 (for all x) is a constant its derivative is 0. 1 is the only value that also makes the right hand side 0.
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