## Sunday, January 5, 2014

### Question of the week #5

This week's post comes from differential equations:
(a). Use integration by parts to show that:
$$\int sinx \cdot cosx \cdot e^{-sinx} dx = -e^{-sinx} \cdot \big( 1 + sinx \big) + c$$
Now consider the following differential equation:
$$\frac{dy}{dx}-y \cdot cosx = sinx \cdot cosx$$
(b). Determine the integration factor and find the general solution $y=f(x)$
(c). Find the special solution satisfying $f(0)=-2$