operadors diferencials amb coeficients constants

d_{x}[y(x)]+a·y(x) = 0
y(x) = e^{(-a)x}


d_{xx}[y(x)]+(a+b)·d_{x}[y(x)]+(ab)·y(x) = 0
( d_{x}[...]+a )o( d_{x}[...]+b )[y(x)] = 0
y(x) = e^{(-a)x}+e^{(-b)x}


x·d_{x}[y(x)]+a·y(x) = 0
y(x) = x^{(-a)}


x·d_{x}[ x·d_{x}[y(x)] ]+(a+b)·x·d_{x}[y(x)]+(ab)·y(x) = 0
( x·d_{x}[...]+a )o( x·d_{x}[...]+b )[y(x)] = 0
y(x) = x^{(-a)}+x^{(-b)}


x^{(p+1)}·d_{x}[y(x)]+a·y(x) = 0
y(x) = e^{(a/p)·(1/x^{p})}


x^{(p+1)}·d_{x}[ x^{(p+1)}·d_{x}[y(x)] ]+(a+b)·x^{(p+1)}·d_{x}[y(x)]+(ab)·y(x) = 0
( x^{(p+1)}·d_{x}[...]+a )o( x^{(p+1)}·d_{x}[...]+b )[y(x)] = 0
y(x) = e^{(a/p)·(1/x^{p})}+e^{(b/p)·(1/x^{p})}


x^{((-p)+1)}·d_{x}[y(x)]+a·y(x) = 0
y(x) = e^{(-1)·(a/p)·x^{p}}


x^{((-p)+1)}·d_{x}[ x^{((-p)+1)}·d_{x}[y(x)] ]+(a+b)·x^{((-p)+1)}·d_{x}[y(x)]+(ab)·y(x) = 0
( x^{((-p)+1)}·d_{x}[...]+a )o( x^{((-p)+1)}·d_{x}[...]+b )[y(x)] = 0
y(x) = e^{(-1)·(a/p)·x^{p}}+e^{(-1)·(b/p)·x^{p}}