Got stuck on a simple ODE

[sanctus]

Ok this might just be because I worked almost non-stop for ten hours, but how do you solve the following differential equation for E(t)?

[math]\frac{dE}{dt}+\frac{da(t)}{dt}/a(t)\cdot E(t)[/math]

 

It's easy to see that the solution is proportional to 1/a(t), but how do you actually find it?

[Qfwfq]

I'm not sure how to read the equation. Is the whole thing = 0 and are a and E both in the denominator?

[sanctus]

Yes i forgot the =0 and E(t)is not in the denominator:

[math] \frac{dE(t)}{dt}+\frac{\frac{da(t)}{dt}}{a(t)} \cdot E(t)=0[/math]

 

Sorry for that.

[Qfwfq]

No problem. :)

 

Have you tried writing it as follows?

 

[math]\frac{d\ln E(t)}{dt}+\frac{d\ln a(t)}{dt}=0[/math]

[sanctus]

No until now, but in this way I see now how it works.

Thanks very much.