ODE
\[ (x-y(x))^2 y'(x)=a^2 \] ODE Classification
[[_homogeneous, `class C`], _dAlembert]
Book solution method
Equation linear in the variables, \(y'(x)=f(a+b x+ c y(x))\)
Mathematica ✓
cpu = 0.485159 (sec), leaf count = 35
\[\text {Solve}[a \log (a-y(x)+x)+2 y(x)+2 c_1=a \log (-a-y(x)+x),y(x)]\]
Maple ✓
cpu = 0.206 (sec), leaf count = 38
\[[y \left (x \right ) = {\mathrm e}^{\RootOf \left (-a \ln \left ({\mathrm e}^{\textit {\_Z}}-2 a \right )+a \textit {\_Z} -2 \,{\mathrm e}^{\textit {\_Z}}+2 \textit {\_C1} +2 a -2 x \right )}-a +x]\] Mathematica raw input
DSolve[(x - y[x])^2*y'[x] == a^2,y[x],x]
Mathematica raw output
Solve[2*C[1] + a*Log[a + x - y[x]] + 2*y[x] == a*Log[-a + x - y[x]], y[x]]
Maple raw input
dsolve((x-y(x))^2*diff(y(x),x) = a^2, y(x))
Maple raw output
[y(x) = exp(RootOf(-a*ln(exp(_Z)-2*a)+a*_Z-2*exp(_Z)+2*_C1+2*a-2*x))-a+x]