4.13.18 \((x-y(x))^2 y'(x)=a^2\)

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 = 0.113989 (sec), leaf count = 35

\[\text {Solve}\left [a \log (a-y(x)+x)+2 c_1+2 y(x)=a \log (-a-y(x)+x),y(x)\right ]\]

Maple
cpu = 0.033 (sec), leaf count = 33

\[ \left \{ y \relax (x ) -{\frac {a\ln \left (y \relax (x ) -x+a \right ) }{2}}+{\frac {a\ln \left (y \relax (x ) -x-a \right ) }{2}}-{\it \_C1}=0 \right \} \] 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),'implicit')

Maple raw output

y(x)-1/2*a*ln(y(x)-x+a)+1/2*a*ln(y(x)-x-a)-_C1 = 0