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?
Separate variables,
d(xy) = ysin(y) dy
Integrate both sides,
xy = ∫ysin(y) dy = -ycos(y) + sin(y) + c <==Answer
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Attn:
∫ysin(y) dy = -ycos(y) + sin(y) + c can be obtained by tabler method or integration by parts.