ODE
\[ k (-a+y(x)+x)^2+(x-a)^2 y'(x)+y(x)^2=0 \] ODE Classification
[[_homogeneous, `class C`], _rational, _Riccati]
Book solution method
Riccati ODE, Generalized ODE
Mathematica ✓
cpu = 0.303777 (sec), leaf count = 34
\[\left \{\left \{y(x)\to \frac {k (a-x)}{k+1}+\frac {1}{\frac {k+1}{a-x}+c_1}\right \}\right \}\]
Maple ✓
cpu = 0.163 (sec), leaf count = 39
\[\left [y \left (x \right ) = \frac {\left (a -x \right ) \left (\textit {\_C1} k \left (a -x \right )-1\right )}{\textit {\_C1} k \left (a -x \right )+\textit {\_C1} \left (a -x \right )-1}\right ]\] Mathematica raw input
DSolve[y[x]^2 + k*(-a + x + y[x])^2 + (-a + x)^2*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (k*(a - x))/(1 + k) + ((1 + k)/(a - x) + C[1])^(-1)}}
Maple raw input
dsolve((x-a)^2*diff(y(x),x)+k*(x+y(x)-a)^2+y(x)^2 = 0, y(x))
Maple raw output
[y(x) = (a-x)*(_C1*k*(a-x)-1)/(_C1*k*(a-x)+_C1*(a-x)-1)]