ODE
\[ x y'(x)=y(x)-x \cos ^2\left (\frac {y(x)}{x}\right ) \] ODE Classification
[[_homogeneous, `class A`], _dAlembert]
Book solution method
Homogeneous equation
Mathematica ✓
cpu = 0.0245053 (sec), leaf count = 17
\[\left \{\left \{y(x)\to x \tan ^{-1}\left (2 c_1-\log (x)\right )\right \}\right \}\]
Maple ✓
cpu = 0.012 (sec), leaf count = 26
\[ \left \{ -{\it \_C1}+{1\sin \left ( {\frac {y \left ( x \right ) }{x}} \right ) \left ( \cos \left ( {\frac {y \left ( x \right ) }{x}} \right ) \right ) ^{-1}}+\ln \left ( x \right ) =0 \right \} \] Mathematica raw input
DSolve[x*y'[x] == -(x*Cos[y[x]/x]^2) + y[x],y[x],x]
Mathematica raw output
{{y[x] -> x*ArcTan[2*C[1] - Log[x]]}}
Maple raw input
dsolve(x*diff(y(x),x) = y(x)-x*cos(y(x)/x)^2, y(x),'implicit')
Maple raw output
-_C1+1/cos(y(x)/x)*sin(y(x)/x)+ln(x) = 0