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 = 0.549997 (sec), leaf count = 27
\[\text {Solve}\left [4 (\log (x)+c_1)=\frac {2 y(x)}{x}+\sin \left (\frac {2 y(x)}{x}\right ),y(x)\right ]\]
Maple ✓
cpu = 0.071 (sec), leaf count = 35
\[\left [\frac {\cos \left (\frac {y \left (x \right )}{x}\right ) \sin \left (\frac {y \left (x \right )}{x}\right ) x +y \left (x \right )}{2 x}-\ln \left (x \right )-\textit {\_C1} = 0\right ]\] 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))
Maple raw output
[1/2*(cos(y(x)/x)*sin(y(x)/x)*x+y(x))/x-ln(x)-_C1 = 0]