ecuació diferencial series

x^{2m}·d_{x...(m)...x}^{m}[y(x)] = y(x)


y(x) = ∑ ( k!·x^{k+m} )


x^{2m}·d_{x...(m)...x}^{m}[ ∑ ( k!·x^{k+m} ) ] = ∑ ( (k+m)!·x^{(k+m)+m} )


p = k+m <==> ∑ ( (k+m)!·x^{(k+m)+m} ) = ∑ ( p!·x^{p+m} )