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Thread: 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 $\displaystyle y^2$ instead -- do this.

    How would I go about solving for $\displaystyle y^2$? So far I've only had problems where I've had to solve for $\displaystyle y$, 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 $\displaystyle y^2$ instead -- do this.

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

    $\displaystyle y\ dy = t^2\ dt$

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

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

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

    And that's solved for $\displaystyle y^2$

    Hope that helped

    Mathemagister
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