Question

Another ODE problem? http://i.imgur.com/vM2iY.jpg

Answer 1

you can separate the variables

Answer 2

I did, I did the question and my answer is slightly different to wolfram's answer.

Answer 3

get all the y's on the left and the x's on the right

Answer 4

I did, let me show you my workings.

Answer 5

did you take a log on the RHS

Answer 6

Ok I kinda not sure on a particular section. I've divided 1/(1+y) and 1/(x^2+1) to both sides and multiplied both sides. To get \[(1/(1+y))dy= 2x(1/x ^{2}+1)dx

Answer 7

\[1/(1+y)dy= 2x(1/(x^2+1)dx\]

Answer 8

thats right

Answer 9

Integrated LHS to get ln 1+y used u subisition on the RHS

Answer 10

I factored out the 2 from 2x to make it easier, however, in the final answer, wolfram makes it disappear

Answer 11

\[\int\frac{1}{1+y}\text dy=\int\frac{2x}{x^2+1}\text dx\]

Answer 12

Yep, factored out the 2 there.

Answer 13

dont factor out that two

Answer 14

you'll want it there\

Answer 15

Ok so, I'll just get ln x^2+1?

Answer 16

\[\text{let } u=1+x^2 \]\[\text du=2x\]
\[\int\frac{2x}{1+x^2}\text dx=\int\frac{\text du}{u}\]
yes

Answer 17

Thank you!