# Solving differential equation…

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

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

• 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 – Marion Crane Feb 3 '15 at 2:39
• Have you looked at examples in your notes or in your textbook? – Bernard Massé Feb 3 '15 at 2:49
• It's a separable equation. Try replacing $y'=\frac{dy}{dt}$ and gathering $y$'s and $t$'s on their own sides. – Milo Brandt Feb 3 '15 at 4:14

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}]

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

$y dy=-4t dt$

Integrate both sides.

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

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