Question

Solve the differential equation dx+(x/y-sin(y))dy=0.

Answer 1

Dividing by dx and simplifying we get,\[y \sin y \times dy = x dy + y dx\]
\[y \sin y \times dy = d(xy)\] exact differential

Now integrate on both sides by using integration by parts.

Answer 2

\[(\frac {x}{y}-sin y)dy =-dx\]
integral both sides
xlny +cos y = -x +C
xlny +cos y +x =C
is it not right? I am new in differential equation. Please, check

Answer 3

No loser66, you cannot integrate both the dependent and independent variable simultaneously.

Answer 4

why? the LHS respect to y, and the RHS respect to x.

Answer 5

I am talking about x/y.

Answer 6

oh yea, thank you. So, we must have x and y separately when calculating, right?

Answer 7

The correct answer is xy+ycos(y)-sin(y)=c but you need to use integrating factor for this problem.

Answer 8

Yes, thats it. Differential equations is a good topic. Try learning it.

Answer 9

Is it compulsory to use integrating factor for this problem? I got the answer in my way.

Answer 10

Thanks, guys.