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Math Help - Initial value Problem

  1. #1
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    Question Initial value Problem

    Help!!!

    Find an implicit and an explicit solution of the given initial value problems.
    a) dy/dt+2y=1, when y(0)=5/2

    b) (1+x^4)dy+x(1+4y^2)dx=0, when y(1)=0


    Thanks a lot!!!
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  2. #2
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    Quote Originally Posted by kithy View Post
    Help!!!

    Find an implicit and an explicit solution of the given initial value problems.
    a) dy/dt+2y=1, when y(0)=5/2

    Mr F says: Many approaches are possible. Here are three:
    1. Use the integrating factor method.
    2. The DE is seperable: dt/dy = 1/(1 - 2y).
    3. First order linear with constant coefficients. Assume a solution of the form y = {\color{red}A e^{\lambda t} + B}. Hint: B = 1/2, A is an arbitrary constant. Now find {\color{red}\lambda}.

    b) (1+x^4)dy+x(1+4y^2)dx=0, when y(1)=0

    Mr F says: The DE is seperable: {\color{red}-\frac{dy}{1 + 4y^2} = \frac{x}{1 + x^4}}. The y-integration is a standard form. For the x-integration, make the substitution u = x^2.

    Thanks a lot!!!
    ..
    Last edited by mr fantastic; June 10th 2008 at 03:52 AM. Reason: Fixed the latex - thanks moo.
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