How to attack this DE

[fitzoyo]

Hi,

I'm struggling to work out what method i can use to solve this DE:

y/4y+2 dy/dx = 3x

I've been looking at using the integrating factor method and also have been looking to use a substitution put can't seem to see through this one. Can anyone offer any advice on which approach i should be looking to use.

Thanks.

 

[galactus]

Hi,

I'm struggling to work out what method i can use to solve this DE:

y/4y+2 dy/dx = 3x

I've been looking at using the integrating factor method and also have been looking to use a substitution put can't seem to see through this one. Can anyone offer any advice on which approach i should be looking to use.

Thanks.

Is there a typo?. What is the y/4y?. This would reduce to \(\displaystyle \frac{y}{4y}=1/4\).

Or is it \(\displaystyle \frac{y}{4}y=\frac{y^{2}}{4}\).

Just making sure.

 

[fitzoyo]

Sorry, not being very clear, should read:

(y/(4y+2)) dy/dx = 3x.

 

[tkhunny]

You MUST be able to see that this is separable.

\(\displaystyle \frac{y}{4y+2}\;dy = 3x\;dx\)

Find some antiderivatives.

\(\displaystyle \frac{y}{2y+1}\;dy = 6x\;dx\)

That might be easier.

\(\displaystyle \left[1 - \frac{1}{2y+1}\right]dy = 12x\;dx\)

Maybe even easier.