I worked through to Y(s) = (4s^3 + 18s^2 + 24s + 13)/(s+1)^4

i need help finding the inverse laplace transform

2. I've tried multiple times to find the general solution of the following equation always ending up at dead ends.

[x^(n+1)y^n + ay]dx + [y^(n+1)x^n + ax]dy = 0

Caution: the answer depends on the numerical value of n

Any help will be much appreciated

Thank you