5 Examples using Frobenius series on first order ode

5.1 Example 1. xy+y=0
5.2 Example 2. xy+y=x
5.3 Example 3. xy+y=1
5.4 Example 4. xy+y=k
5.5 Example 5. xy+y=sinx
5.6 Example 6. xy+y=x+x3+2x4
5.7 Example 7. xy+y=1x
5.8 Example 9. xy+y=1x2
5.9 Example 10. xy+y=3+x
5.10 Example 11. xy+y=1x3
5.11 Example 11. y+xy=x2