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# vectors eigenvectors P6 Q watch

1. okay....

given that

y (d^2y/dx^2) + (dy/dx)^2 + y = 0

how do I find an expression for d^3y/dx^3

is it:

(d^3y/dx^3) + dy/dx = 0

??

And how then, given that y = 1 and dy/dx = 1 at x = 0

do I find the series solution for y in ascending powers of x, up to and including the term in x^3

??
2. (Original post by lesser weevil)
okay....

given that

y (d^2y/dx^2) + (dy/dx)^2 + y = 0

how do I find an expression for d^3y/dx^3

is it:

(d^3y/dx^3) + dy/dx = 0

??

And how then, given that y = 1 and dy/dx = 1 at x = 0

do I find the series solution for y in ascending powers of x, up to and including the term in x^3

??
I think you just differentiate with respect to x again:

y(d^2y/dx^2) + (dy/dx)^2 + y = 0

i.e.

(dy/dx)(d^2y/dx^2) + y(d^3y/dx^3) + 2(dy/dx)(d^2y/dx^2) + (dy/dx) = 0

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