On the Derivation of a Closed-Form Expression for the Solutions of a Subclass of Generalized Abel Differential Equations

Table 1

The polynomial of the right-hand side of (13) for various values of 𝑘.

𝑘	𝑔(𝑦(𝑡))
2	−𝑦(𝑡)^3+𝑦(𝑡)^2
3	2𝑦(𝑡)^4−4𝑦(𝑡)^3+2𝑦(𝑡)^2
4	3𝑦(𝑡)^5−6𝑦(𝑡)^4+3𝑦(𝑡)^3
5	−6𝑦(𝑡)^6+18𝑦(𝑡)^5−18𝑦(𝑡)^4+6𝑦(𝑡)^3
6	−10𝑦(𝑡)^7+30𝑦(𝑡)^6−30𝑦(𝑡)^5+10𝑦(𝑡)^4
7	20𝑦(𝑡)^8−80𝑦(𝑡)^7+120𝑦(𝑡)^6−80𝑦(𝑡)^5+20𝑦(𝑡)^4
8	35𝑦(𝑡)^9−140𝑦(𝑡)^8+210𝑦(𝑡)^7−140𝑦(𝑡)^6+35𝑦(𝑡)^5