ODE
\[ y'''(x)=\cos (x)+1 \] ODE Classification
[[_3rd_order, _quadrature]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0319679 (sec), leaf count = 29
\[\left \{\left \{y(x)\to c_3 x^2+c_2 x+c_1+\frac {x^3}{6}-\sin (x)\right \}\right \}\]
Maple ✓
cpu = 0.01 (sec), leaf count = 24
\[ \left \{ y \left ( x \right ) ={\frac {{x}^{3}}{6}}-\sin \left ( x \right ) +{\frac {{\it \_C1}\,{x}^{2}}{2}}+{\it \_C2}\,x+{\it \_C3} \right \} \] Mathematica raw input
DSolve[y'''[x] == 1 + Cos[x],y[x],x]
Mathematica raw output
{{y[x] -> x^3/6 + C[1] + x*C[2] + x^2*C[3] - Sin[x]}}
Maple raw input
dsolve(diff(diff(diff(y(x),x),x),x) = 1+cos(x), y(x),'implicit')
Maple raw output
y(x) = 1/6*x^3-sin(x)+1/2*_C1*x^2+_C2*x+_C3