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

I know that the integrating factor is y.

y dx+x dy-ysin(y) dy=0

d(xy)-ysin(y) dy=0

How do I integrate this?

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

I know that the integrating factor is y.

y dx+x dy-ysin(y) dy=0

d(xy)-ysin(y) dy=0

How do I integrate this?

Tutors, please sign in to answer this question.

Separate variables,

d(xy) = ysin(y) dy

Integrate both sides,

xy = ∫ysin(y) dy = -ycos(y) + sin(y) + c <==Answer

-------

Attn:

∫ysin(y) dy = -ycos(y) + sin(y) + c can be obtained by tabler method or integration by parts.

Hilton T.

Master teacher/tutor of Math, physics, and Chemistry

New Rochelle, NY

5.0
(115 ratings)

Samuel H.

Professional Math Tutor

Brooklyn, NY

5.0
(146 ratings)