ODE
\[ x y'(x)+\cos \left (y'(x)\right )=y(x) \] ODE Classification
[_Clairaut]
Book solution method
Clairaut’s equation and related types, main form
Mathematica ✓
cpu = 0.00992181 (sec), leaf count = 13
\[\left \{\left \{y(x)\to c_1 x+\cos \left (c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.022 (sec), leaf count = 31
\[ \left \{ y \left ( x \right ) -\arcsin \left ( x \right ) x-\sqrt {-{x}^{2}+1}=0,y \left ( x \right ) =\cos \left ( {\it \_C1} \right ) +{\it \_C1}\,x \right \} \] Mathematica raw input
DSolve[Cos[y'[x]] + x*y'[x] == y[x],y[x],x]
Mathematica raw output
{{y[x] -> x*C[1] + Cos[C[1]]}}
Maple raw input
dsolve(cos(diff(y(x),x))+x*diff(y(x),x) = y(x), y(x),'implicit')
Maple raw output
y(x)-arcsin(x)*x-(-x^2+1)^(1/2) = 0, y(x) = cos(_C1)+_C1*x