Nalezn�te v�echna maxim�ln� �e�en� n�sleduj�c�ch diferenci�ln�ch
rovnic, zn�te-li n�kter� jejich �e�en�
$$
xy'' + 2y'  -xy = 0, \quad y_1(x) = \frac{e^x}{x}, 
$$

$$
x^2 (x+1)y'' - 2y = 0, \quad y_1 (x) = 1 + \frac 1x,
$$

$$
(1+x^2)y'' + 2xy' - 2y = 0, \quad y_1(x) = x, \qquad
$$

$$
xy''' - y'' - xy' + y = 0, \quad y_1(x) = x, \quad y_2(x) = e^x \quad .
$$

