Solve the given differential equation by separation of variables. \csc y

Efan Halliday

Efan Halliday

Answered question

2021-10-21

Solve the given differential equation by separation of variables.
cscydx+sec2xdy=0

Answer & Explanation

doplovif

doplovif

Skilled2021-10-22Added 71 answers

cscydx+sec2xdy=0
Rearrange terms
sec2xdy=cscydx
Separate the variables
dycscy=1sec2xdx
siny=cos2xdx
Integrate both sides
siny=cos2xdx
Use the identity cos2x=1+cos2x2, so
siny=(1+cos2x2)dx
Distribute
siny=(12+cos2x2)dx
siny=12dx12cos2xdx
Rewrite
siny=12dx12(2)cos2xcosu(2)dxdu
Apply sinudu=cosu+C and cosudu=sinu+C
cosy=12x14sin2x+C
Multiply both sides by -4
4cosy=2x+sin2x+C
Result:
4cosy=2x+sin2x+C

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?