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There is this differential equation that I could not solve. Can someone please help me solve it?

$$y'=-\frac{4t}{y}$$

Thanks in advance!

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  • $\begingroup$ Oh hell. I have been thinking about it for half an hour and it didn't stuck me. Im having a bad day. thanks @Fundamental $\endgroup$ – Marion Crane Feb 3 '15 at 2:39
  • $\begingroup$ Have you looked at examples in your notes or in your textbook? $\endgroup$ – Bernard Massé Feb 3 '15 at 2:49
  • $\begingroup$ It's a separable equation. Try replacing $y'=\frac{dy}{dt}$ and gathering $y$'s and $t$'s on their own sides. $\endgroup$ – Milo Brandt Feb 3 '15 at 4:14
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If y=y(t)...

[\begin{array}{l} \frac{{dy}}{{dt}} = - \frac{{4t}}{y}\\ ydy = - 4tdt\\ \int {ydy = - 4\int {tdt} } \\ \frac{{{y^2}}}{2} = - 2{t^2} + c\\ y = \sqrt { - 4{t^2} + c} \end{array}]

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$\frac{dy}{dt}=\frac{-4t}{y}$

$y dy=-4t dt$

Integrate both sides.

$\frac{y^2}{2} = -2t^2+c$

$y^2=-4t^2+c$

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