My nswer is so wrong yet again.

2du/dt=u^2, u(0)=1

Separating the variables, we have

1/(u^2) du  = (1/2)dt       Now integrate

∫u^-2 du = ∫ (1/2) dt

-1/u = (1/2)t + C    so we have

1/u = -((1/2)t + C) = -(t + 2C)/2

u(t) = -2/(t + 2C)

And

u(0) = 1

So

-2/(0 + 2C)  = 1

-1 = C

So we have

u = -2/(t - 2)   or

u = 2/(2 - t)

Method 1:

2 du / dt = u^2

2du = u^2 dt (Only divide by u^2 leaving the 2 alone) -->

2/u^2 du = dt

2u^-2 du = dt

2*(u^-1)/-1 --> -2/ u = t + C (Integrate)

u(t + C) = -2 --> u = -2 / (t + C)

1 = -2 / ((0) + C)

1 = -2 / C

C = -2

u = -2 / (t - 2)

u = 2 / -(t - 2)

u = 2 / (-t + 2)

u = 2 / (2 - t).

Method 2:

du/u^2 = 1/2 dt (this time we divided by 2 AND u^2)

u^-2 du = 1/2 dt

-1/u = (1/2t) + C

u = -1/((1/2t) + C)

1 = -1/((1/2(0)) + C)

1 = -1/(C)

C = -1

u = -1/(1/2t - 1).

I would try to rearrange and see how "u" could be solved for faster depending on the simplicity of the integration...also the 2nd method has the simplest form without even doing anything...

I cannot see why in solution 1 that t+ c falls onto the denominator or why in solution 2 the -1 goes to the numirator. Thank you for the assistance today. Long day for how much i have done. Next i need to resolve null members and null joints. Oh before that i have to work on understanding the integration factor which seems not to hard if i follow the steps. One hopes anyway.

Stu, maybe you should consider a change in major. You could take bartending classes. Here, you could make a fair living by wage and tips. I think you might do ok at this after a few years of practice.

The chimp bartender, I comment on, made great tips –mostly bananas, but cash too. After he retired, he lived quite well. He was one of the few who could actually pay for his keep and his keepers. Those who polished his gold-plated monkey bars to a mirror like shine, were his most prized and favored keepers. He rewarded them well, too.

Just something for you to consider.

Dear Anonymous, better than being an a*s like you. You do not know anythimg about me or where I could be coming from. You are a complete a*s. Go eat some hay or something.

I hope your posts make you feel taller! They definatly make me feel happy for my accomplisment and my studying. You keep on telling your self you are tall. Sure you will get there one day when you develop respect for others and what they do as well as for effort they make to reach there goals; and when you don't need to hide from what you say.

A*s:

a hoofed mammal of the horse family, which is typically smaller than a horse and has longer ears and a braying call.

synonyms:donkey; 

From Stu. 

Go troll someone else you 4 ft tall a*s.

That is about the height of a bonobo chimpanzee, isn't it?

They are very social chimps. I'm not sure if they make good bartenders. Though maybe it would make a good mate for you, and even help with bartending like reminding you to pick up your banana peals and such.

Moderators please delete the posts that are disrailing the thread. 

Oh please don’t delete these. They are so funny. I have not ever read troll posts as funny as the ones on this site. The chimp and banana ones still make me laugh.

I don’t mean to be rude to you Stu, but these really are funny. Think about all the people on here who might be a target and this troll picks you. In a way, it is really a compliment. Your answers make them more funny. Until you made this post, I thought you might be doing it to yourself. Maybe that’s part of it. If you are the one doing it, it is truly funny and awesome.

The most funny one on here is not even a troll post. It’s from a girl named Charlotte. She compliments CPhill and then talks about how someone made a coconut look like her grandmother. She uses bad language, but that is just the way she talks and writes, and I do not think she meant to be offensive. I do think she meant to be sincere. I laughed so hard, I about stabbed myself with a paint brush.

I am an art major. I learn a lot of maths here, but I mainly understand and appreciate art. I really like the art of humor on here. Even your trolls are great fun.

My first post is not about math, but a troll. That is funny too. It is the art of humor, I guess.

I agree with Stu that you are an a*s and a coward anoymous----> http://m.youtube.com/watch?v=GWSZ1DKjNzY!

I don't recommend someone to agree with and promotes asses on this site Gingerale as it takes away from hard work the volunteers do.

In method 1: -2/ u = t + C --> if we cross multiply we get -2 = u(t+C)

then, we divide both sides by (t+C) -- treat them like one variable since the constant is just along with the t, now, we get u = -2/(t+C)

Same for method 2: you just have to treat them as if they are one variable and cross multiply and divide.

I see Phill. Thanks also Aziz. I will go through these a bit more this morning and might hit a few walls as i move along into the next questions and i've such limited time to do everything now. 

Lol at a first post from Gingerale. Awesome first post to make your presence felt.

I have tried again his morning and struggled with this one again.