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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 $f(0)=-2$

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