ODE
\[ y'''(x)+y'(x)=x^3+\cos (x) \] ODE Classification
[[_3rd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.251854 (sec), leaf count = 39
\[\left \{\left \{y(x)\to \frac {x^4}{4}-3 x^2-\frac {1}{2} (x+2 c_2) \cos (x)+(1+c_1) \sin (x)+c_3\right \}\right \}\]
Maple ✓
cpu = 0.662 (sec), leaf count = 32
\[\left [y \left (x \right ) = \frac {x^{4}}{4}-\textit {\_C2} \cos \left (x \right )+\sin \left (x \right ) \textit {\_C1} -3 x^{2}+\sin \left (x \right )-\frac {x \cos \left (x \right )}{2}+\textit {\_C3}\right ]\] 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))
Maple raw output
[y(x) = 1/4*x^4-_C2*cos(x)+sin(x)*_C1-3*x^2+sin(x)-1/2*x*cos(x)+_C3]