Second order

[Anthonyk2013]

I'm confused about step 5 in my book. Where did 16ke^4x-8ke^4x come from. I know it's something simple I'm over looking.

 

[ksdhart]

Unfortunately, that picture is far too small for me to make out anything meaningful. Can you please post a bigger picture, or type out the relevant information? Thank you.

 

[Anthonyk2013]

Hope this image is better



Apologies problem with that image as well :c

 

[Anthonyk2013]

Still not the best. Busy morning I'll try again later to upload a better image.

The area I'm in trouble is the use of the product rule on the second image.

 

[ksdhart]

Well, I'm still finding it difficult to follow exactly what's going on. But my best guess is that D is shorthand for dy/dx. From context, we know that D = 4, because D² = 16 and 2D = 8. But I'm confused here as well, because that doesn't match up with the information given at the very beginning of the problem. I can't really read it well, but it says something like:

Solve the equation \(\displaystyle \frac{d^2y}{dx^2}-2\frac{dy}{dx}+y=3e^{4x}\), given the boundary condition that when x = 0, y = [??] and dy/dx = 4 [??]

It says 4, and I distinctly see some fraction after that, but I can't read it well enough to guess what fraction it might be, nor the specified value of y.