Using the substitution $p=x+y$, find the general solution of $dy/dx=(3x+3y+4)/(x+y+1)$. Using the substitution $p=x+y$, find the general solution of $$\frac{dy}{dx}=(3x+3y+4)/(x+y+1)$$
Here are my steps:
Since $p=x+y$, $$\frac{3x+3y+4}{x+y+1}=\frac{3p+4}{p+1}=\frac{1}{p+1}+3$$
Therefore, integrate both sides 
$$y=\ln(p+1)+3p+c$$
$$y=\ln(x+y+1)+3(x+y)+c$$
But the answer in my book is $$x+y-\frac{1}{4}\ln(4x+4y+5)=4x+c$$
Is that correct?

For the left hand side of your differential equation, you should substitute $ \frac{dy}{dx} = \frac{dp}{dx} - 1\,, $ since $ p = x + y $, and then advance with your solution by separation of variable method. 
