# Thread: help plz!

1. ## help plz!

I been working on this forever. I am stuck at the integration part.
the problem is:

cosysint dy/dt = sinycost

y=arcsin(C sint)

Here is my attempt :
cosy/siny dy = cost/sint dt

arctany dy = arctant dt

then i integrate both side and get

yarctany-1/2ln(1+y^2)=tarctant-1/2ln(1+t^2)

some there i am stuck.. i dunno how to get the answer y=arcsin(c sint)

2. The D.E. is...

$\cot y\cdot dy = \cot t\cdot dt$

Taking into account that is...

$\int \cot t\cdot dt = \ln \sin t + \ln c$

... we can separate variables and integrate, so that we obtain...

$\ln \sin y = \ln \sin t + \ln c \rightarrow \sin y = c\cdot \sin t \rightarrow y = \sin ^{-1} (c\cdot \sin t)$

Kind regards

$\chi$ $\sigma$

3. thanks alot...