Question

dy/dx=sinxcosy how to find y?

Answer 1

One way to do it is to get the dy on the same side as the y term and to get dx on the same side as the x term:
\[\frac{dy}{\cos(y)}=\sin(x)dx\]From here, you can integrate both sides. The right side is fairly straightforward, and we get
\[\int\limits{\frac{dy}{\cos(y)}}=\int\limits{\sin(x)dx}\]\[\int\limits{\frac{dy}{\cos(y)}}=-\cos(x)+K\]
Now for the left side, the reciprocal of the cosine is the secant, so we have
\[\int\limits{\sec(y)dy}=-\cos(x)+K\]
Integrate (if you need help with this integral, click here: http://math2.org/math/integrals/more/sec.htm)
\[\ln|\sec(y)+\tan(y)|=-\cos(x)+C\]
Solve for y, if your professor/teacher requires it.