This week's post comes from differential equations:

$$

\int sinx \cdot cosx \cdot e^{-sinx} dx = -e^{-sinx} \cdot \big( 1 + sinx \big) + c

$$

$$

\frac{dy}{dx}-y \cdot cosx = sinx \cdot cosx

$$

**(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**$f(0)=-2$
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