Integrating Factor making DE Exact

**exphate** · August 29th 2009, 03:46 AM

Hello hello!

I'm having trouble with more homework questions. This time, it's a DE that needs an IF to make it exact. Here it is

$\frac{x}{2} dt + (t + t^{\frac{1}{2}}sinx)dx = 0$

Anyone able to help?

**Jester** · August 29th 2009, 06:23 AM

Originally Posted by exphate

Hello hello!

I'm having trouble with more homework questions. This time, it's a DE that needs an IF to make it exact. Here it is

$\frac{x}{2} dt + (t + t^{\frac{1}{2}}sinx)dx = 0$

Anyone able to help?

The integrating factor is

$\mu = \frac{1}{\sqrt{t}}$ ,

although, if you write your ODE as

$\frac{dt}{dx} + \frac{2t}{x} = - \frac{2 \sqrt{t} \sin x}{x}$

the ODE is Bernoulli.

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