ODE
\[ x y'(x)+\tan (y(x)+x)+x=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries]]
Book solution method
Change of Variable, new dependent variable
Mathematica ✓
cpu = 0.0768081 (sec), leaf count = 16
\[\left \{\left \{y(x)\to \sin ^{-1}\left (\frac {c_1}{x}\right )-x\right \}\right \}\]
Maple ✓
cpu = 0.081 (sec), leaf count = 59
\[ \left \{ {\frac { \left ( -{\it \_C1}\,{x}^{2}+ \left ( \tan \left ( x \right ) \right ) ^{2}+1 \right ) \left ( \tan \left ( y \left ( x \right ) \right ) \right ) ^{2}-2\,\tan \left ( x \right ) \tan \left ( y \left ( x \right ) \right ) {\it \_C1}\,{x}^{2}+1+ \left ( -{\it \_C1}\,{x}^{2}+1 \right ) \left ( \tan \left ( x \right ) \right ) ^{2}}{ \left ( \tan \left ( x \right ) +\tan \left ( y \left ( x \right ) \right ) \right ) ^{2}{x}^{2}}}=0 \right \} \] Mathematica raw input
DSolve[x + Tan[x + y[x]] + x*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -x + ArcSin[C[1]/x]}}
Maple raw input
dsolve(x*diff(y(x),x)+x+tan(x+y(x)) = 0, y(x),'implicit')
Maple raw output
((-_C1*x^2+tan(x)^2+1)*tan(y(x))^2-2*tan(x)*tan(y(x))*_C1*x^2+1+(-_C1*x^2+1)*tan(x)^2)/(tan(x)+tan(y(x)))^2/x^2 = 0