# What is the standard method for finding solutions of differential equations such as this one? (if th

What is the standard method for finding solutions of differential equations such as this one? (if there is any)
$x{y}^{\prime }={y}^{2}-\left(2x+1\right)y+{x}^{2}+2x$
where $y=ax+b$ is a particular solution.
Do I substitute $y$ with $ax+b+u\left(x\right)$ and then search for a solution or am I not noticing something and there's quicker way?
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bap1287dg
I think that your hint is "there exists $a,b$ such thaht $y\left(x\right)=ax+b$ is solution". We find easily that $y\left(x\right)=x$ and $y\left(x\right)=x+1$ are solutions.
Hint: Note that your equation is
$x{y}^{\mathrm{\prime }}\left(x\right)-x=\left(y\left(x\right)-x\right)\left(y\left(x\right)-x-1\right)$
Now put $y\left(x\right)=x+z\left(x\right)$.