Question

solve y'+Y/(x+9)=(x+9)^4

Answer 1

I'm thinking of doing a simple integrating factor method here, but I'm not sure if I could do a Bernoulli's equation or not

Answer 2

I think integrating factor is okay.
\[y'+\frac{y}{(x+9)}=(x+9)^4\]\[\alpha = e^{\int \frac{1}{x+9}dx}=e^{\ln (x+9)}=x+9\]
\[y=\frac{1}{x+9}\int(x+9)(x+9)^4dx=\frac{1}{x+9}\int(x+9)^5dx=...\]