[Darkening Light]

I was solving a differential equation and got to the step where I had to integrate. I did it two different methods to get two different answers. I was wondering if anyone knows why one method must not work.

Method 1



let

therefore:







so:





Method 2







As you see both gives different answer but I'm sure both methods are correct.

Thanks,
Kieron

[little_wizard123]

You missed off the '+c'. Your first answer is equivalent to 1/4*ln(4) + 1/4*ln(y).

[nuodai]

The key is the "+C", which you forgot to add.

Notice that if then , so when you integrate two things then you can end up with two different answers, but they will always only differ by a constant.

Here, , so you get . The is a constant, and so (if you add your constants of integration) the two answers are actually the same -- this can then be absorbed into the constant of integration in your first method to give .

[Hopple]

You've forgotten your constant of integration.

[Darkening Light]

(Original post by nuodai)
The key is the "+C", which you forgot to add.

Notice that if then , so when you integrate two things then you can end up with two different answers, but they will always only differ by a constant.

Here, , so you get . The is a constant, and so (if you add your constants of integration) the two answers are actually the same -- this can then be absorbed into the constant of integration in your first method to give .

I can't believe something so simple drove me crazy. Most of the times the constant doesn't change the answer so I tend to forget to put it.

Thanks

[Jodin]

(Original post by Darkening Light)
I can't believe something so simple drove me crazy. Most of the times the constant doesn't change the answer so I tend to forget to put it.

Thanks

Indeed! In regards to forgetting about the constant, try integrating 1/x dx by parts some time, with u = 1/x, v' = 1.

[pi+e=pie]

the +c my friend!
i forgot it when integrating arcsin and i got two different answers by two methods aswell.
not to worry, just an easy mistake