ODE
\[ x y'(x)=y(x)+x \sec ^2\left (\frac {y(x)}{x}\right ) \] ODE Classification
[[_homogeneous, `class A`], _dAlembert]
Book solution method
Homogeneous equation
Mathematica ✓
cpu = 0.0441468 (sec), leaf count = 27
\[\text {Solve}\left [4 \left (c_1+\log (x)\right )=\frac {2 y(x)}{x}+\sin \left (\frac {2 y(x)}{x}\right ),y(x)\right ]\]
Maple ✓
cpu = 0.02 (sec), leaf count = 35
\[ \left \{ {\frac {1}{2\,x} \left ( \cos \left ( {\frac {y \left ( x \right ) }{x}} \right ) \sin \left ( {\frac {y \left ( x \right ) }{x}} \right ) x+y \left ( x \right ) \right ) }-\ln \left ( x \right ) -{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[x*y'[x] == x*Sec[y[x]/x]^2 + y[x],y[x],x]
Mathematica raw output
Solve[4*(C[1] + Log[x]) == Sin[(2*y[x])/x] + (2*y[x])/x, y[x]]
Maple raw input
dsolve(x*diff(y(x),x) = y(x)+x*sec(y(x)/x)^2, y(x),'implicit')
Maple raw output
1/2*(cos(y(x)/x)*sin(y(x)/x)*x+y(x))/x-ln(x)-_C1 = 0