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 = 0.150459 (sec), leaf count = 13
\[\{\{y(x)\to c_1 x+\cos (c_1)\}\}\]
Maple ✓
cpu = 0.031 (sec), leaf count = 27
\[\left [y \left (x \right ) = \arcsin \left (x \right ) x +\sqrt {-x^{2}+1}, y \left (x \right ) = \cos \left (\textit {\_C1} \right )+\textit {\_C1} x\right ]\] 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))
Maple raw output
[y(x) = arcsin(x)*x+(-x^2+1)^(1/2), y(x) = cos(_C1)+_C1*x]