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June 17th, 2017, 12:32 PM   #1
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A beginner differential equation question

What is a differential equation ?

It is an equation involving an unknown function (solution) and its derivatives .



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June 17th, 2017, 12:51 PM   #2
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The function (of x) is y, and dy/dx is its derivative (with respect to x).
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June 17th, 2017, 04:33 PM   #3
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If you are asking whether $\displaystyle y= \pm\sqrt{\frac{2}{3}x^3+ C}$ really does satisfy $\displaystyle \frac{dy}{dx}= \frac{x^2}{y}$, it is easy to check. First, squaring both sides gives $\displaystyle y^2= \frac{2}{3}x^3+ C$ and differentiating both sides with respect to x, $\displaystyle 2y\frac{dy}{dx}= 2x^2$. Dividing both sides by 2y, $\displaystyle \frac{dy}{dx}= \frac{x^2}{y}$, precisely the differential equation you started with.

Or, more directly but more complicated, differentiating the original formula with respect to x, $\displaystyle \frac{dy}{dx}= \pm\frac{1}{2}\left(\frac{2}{3}x^3+ C\right)^{-1/2}(2x^2)= \frac{x^2}{\pm\sqrt{\frac{2}{3}x^3+ C}}= \frac{x^2}{y}$.
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Last edited by skipjack; June 17th, 2017 at 05:16 PM.
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June 17th, 2017, 10:17 PM   #4
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Thanks ,

Found some good materials here

National Council Of Educational Research And Training :: Home

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