Solve 2xcosydx+x^2(secy-siny)dx

$$2 x \cos y d x + x ^ { 2 } ( \sec y - \sin y ) d x$$

Factor

$$x\left(dx^{2}\left(\frac{1}{\cos(y)}-\sin(y)\right)+2\cos(dxy)\right)$$

Solution Steps

Factor out x.

$$x\left(2\cos(ydx)+\left(\frac{1}{\cos(y)}-\sin(y)\right)dx^{2}\right)$$

Evaluate

$$\frac{x\left(4\cos(y)\cos(dxy)-dx^{2}\sin(2y)+2dx^{2}\right)}{2\cos(y)}$$