Vreau să prezint, în engleză un mic ghid pentru un anumit tip de probleme. Nu voi face multe explicaţii, voi oferi doar metoda de rezolvare.
Knowing Abel’s theorem,

If  y1(t) and y2(t) are two solutions to

y''+py'+qy=0

then the Wronskian of the two solutions is

W(y_1,y_2)(t)=W(y_1,y_2)(t_0)*e^{-int_{t_0}^{t} p(t)dt}

for some t0.

Suppose We have an equation of the form t^4y''-2t^3-t^8y=0 divide both sides by t^4 to get

y''-frac{2}{t}y'-t^4y=0

Now we can easily apply Abel’s theorem keeping in mind that the wronskian of two functions computed at any point is just some ordinary constant so

W(y_1,y_2)(t)=W(y_1,y_2)(t_0)*e^{int p(t)dt}=c*e^{-int_{t_0}^{t} frac{-2}{t}dt}

Since we have a fast computation course here, lets take the minus two out of the integral, integrate and substitute to get

W(y_1,y_2)(t)=c*e^{2*(lnt-ln(t_0))} =frac{c*e^{2ln(t)}}{e^{2ln(t_0)}}

But since t0 is a constant then e^{2ln(t_0)}=c so we can rewrite our wronskian as being equal to :

W(y_1,y_2)(t)=c*e^{2lnt}=c*e^{lnt^2}=ct^2

W(y_1,y_2)(t)=W(y_1,y_2)(t_0)*e^{int p(t)dt}=c*e^{-int_{t_0}^{t} frac{-2}{t}dt}