1
vote
1answer
31 views

Finding a y(x) that satisfies $ y(x) = \int_0^x \! \left(\frac{t} {y(t)+1}\right)^2 \, \mathrm{d}t $

I'm having problem with finding a y(x) that satisfies $$ y(x) = \int_0^x \! \left(\frac{t} {y(t)+1}\right)^2 \, \mathrm{d}t $$ Here is what I tried to do. $$ y(x) = \int_ \! \left(\frac{x} ...
4
votes
0answers
142 views

Finding a series of functions orthogonal to all $x^{2n}$ but one

We need to find a series of functions $f_m$ verifying the property $$\int_{-\infty}^{+\infty}\! x^{2n} f_m\!(x) \;{\text d}x=\delta_{nm}.$$ We already have found $$f_0(x) = ...