ecuació diferencial series

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


y(x) = ∑ ( 1/( ((n+m)·k+(n+1))...(m)...((n+m)·k+(n+m)) )! )·x^{(n+m)·(k+1)} )


d_{x...(m)...x}^{m}[ ∑ ( 1/( ((n+m)·k+(n+1))...(m)...((n+m)·k+(n+m)) )! )·x^{(n+m)·(k+1)} ) ] = ...
... ∑ ( 1/( ((n+m)·(k+(-1))+(n+1))...(m)...((n+m)·(k+(-1))+(n+m)) )! )·x^{(n+m)·k+n} ) = ...
... ∑ ( 1/( ((n+m)·p+(n+1))...(m)...((n+m)·p+(n+m)) )! )·x^{(n+m)·(p+1)+n} ) & p = k+(-1)