ODE
\[ y'''(x)+y'(x)=x^3+\cos (x) \] ODE Classification
[[_3rd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.113436 (sec), leaf count = 39
\[\left \{\left \{y(x)\to \left (c_1+1\right ) \sin (x)-\frac {1}{2} \left (2 c_2+x\right ) \cos (x)+c_3+\frac {x^4}{4}-3 x^2\right \}\right \}\]
Maple ✓
cpu = 0.063 (sec), leaf count = 36
\[ \left \{ y \left ( x \right ) ={\frac { \left ( -2\,x-4\,{\it \_C2} \right ) \cos \left ( x \right ) }{4}}+{\frac { \left ( 4\,{\it \_C1}+4 \right ) \sin \left ( x \right ) }{4}}+{\frac {{x}^{4}}{4}}-3\,{x}^{2}+{\it \_C3} \right \} \] Mathematica raw input
DSolve[y'[x] + y'''[x] == x^3 + Cos[x],y[x],x]
Mathematica raw output
{{y[x] -> -3*x^2 + x^4/4 + C[3] - ((x + 2*C[2])*Cos[x])/2 + (1 + C[1])*Sin[x]}}
Maple raw input
dsolve(diff(diff(diff(y(x),x),x),x)+diff(y(x),x) = x^3+cos(x), y(x),'implicit')
Maple raw output
y(x) = 1/4*(-2*x-4*_C2)*cos(x)+1/4*(4*_C1+4)*sin(x)+1/4*x^4-3*x^2+_C3