Differential Equations | Frobenius' Method -- Example 1

From the desert, we present an example of a Frobenius series solution to a second order homogeneous differential equation.

[nikitakipriyanov]

so in the end we found that y(x|-2)=1/x², now it's possible to use an Abel's identity to find a "closed form" for other linear independent solution, instead of series with cube root. That would be (if I didn't make any mistakes): y₁(x)=1/x² (x/(x+3))^(7/3).

[branwave]

3:05 That doesn't factor right. To quickly see why, multiply the numbers 2 and 3 which results in a different sign for the constant term (2 * 3 != -6).