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Math Help - IVP

  1. #1
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    IVP

    If we use separation of variables to try to solve the IVP

    we would obtain a solution that could not be put in explicit form. But we can solve for y^2 instead -- do this.

    How would I go about solving for y^2? So far I've only had problems where I've had to solve for y, and I'm not sure what to do here.
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  2. #2
    Member mathemagister's Avatar
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    Quote Originally Posted by cdlegendary View Post
    If we use separation of variables to try to solve the IVP

    we would obtain a solution that could not be put in explicit form. But we can solve for y^2 instead -- do this.

    How would I go about solving for y^2? So far I've only had problems where I've had to solve for y, and I'm not sure what to do here.
    \frac{dy}{dt}=\frac{t^2}{y}

    y\ dy = t^2\ dt

    Integrate both sides: \int y\ dy = \int t^2\ dt

    \frac{y^2}{2} + K_1 = \frac{t^3}{3} + K_2

    y^2 = \frac{2t^3}{3} + C

    And that's solved for y^2

    Hope that helped

    Mathemagister
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