Question

I have to find the solution that satisfies the initial condition y(0)=0
\[ln y + \frac{y^{2}}{2}= sin x +C\]

Answer 1

does that mean I did the integration wrong? this is a continuation of the previous problem

Answer 2

maybe

Answer 3

\[\frac{dy}{dx}=\frac{ycosx}{1+y^{2}}\]

Answer 4

So you did integration be use of separating the variables right?

Answer 5

yes ma'am

Answer 6

\[\int \frac{1+y^{2}}{y}dy= sinx +C\]

Answer 7

\[ln y + \frac{y^{2}}{2}= sin x +C\]

Answer 8

hmm...
y(0)=0 will not work as the initial condition

Answer 9

sorry y(0)= 1

Answer 10

oh! :)
replace x with 0 and y with 1
:)
that will work

Answer 11

And then solve for C

Answer 12

yeah!!!! .5?

Answer 13

yep yep that is the value for C :)

Answer 14

So just write your equation over replacing C with .5

Answer 15

sounds good, thanks!