fp2, some ****ed up differentiation question Watch

anus eater
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Report Thread starter 7 years ago
y(d^2y/dx^2) + (dy/dx)^2 + y = 0

Find an expression for d^3y/dx^3

differentiating (product rule for y(d^2y/dx^2)):
(d^2y/dx)(dy/dx) + y(d^3y/dx^3) + d^3y/dx^3 + y(dy/dx) = 0

typing that alone required more effort than trying to sneeze, masturbate and take a **** at the same time (and i'm guessing i've already gone wrong too according to the mark scheme), so just put me out of my misery . what did i do wrong?
Badges: 14
Report 7 years ago
You differentiated \left( \dfrac{dy}{dx} \right)^2 and y incorrectly. For the first you can use the chain rule, and the second is trivial (because \dfrac{d}{dx}(y) = \dfrac{dy}{dx}).

With these things I prefer to write it using dash notation; that is:

yy'' + (y')^2 + y = 0

Then when you differentiate anything you just increase the number of dashes; so for example, when you differentiate yy'' you get y'y'' + yy''' (this is the part you did correctly). You just need to differentiate (y')^2 and y and then rearrange the resulting equation to make y''' the subject.

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