ODE
\[ y''''(x)=x \cos (x) \] ODE Classification
[[_high_order, _quadrature]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0351655 (sec), leaf count = 32
\[\left \{\left \{y(x)\to c_4 x^3+c_3 x^2+c_2 x+c_1-4 \sin (x)+x \cos (x)\right \}\right \}\]
Maple ✓
cpu = 0.023 (sec), leaf count = 29
\[ \left \{ y \left ( x \right ) =-4\,\sin \left ( x \right ) +x\cos \left ( x \right ) +{\frac {{x}^{3}{\it \_C1}}{6}}+{\frac {{x}^{2}{\it \_C2}}{2}}+{\it \_C3}\,x+{\it \_C4} \right \} \] Mathematica raw input
DSolve[y''''[x] == x*Cos[x],y[x],x]
Mathematica raw output
{{y[x] -> C[1] + x*C[2] + x^2*C[3] + x^3*C[4] + x*Cos[x] - 4*Sin[x]}}
Maple raw input
dsolve(diff(diff(diff(diff(y(x),x),x),x),x) = x*cos(x), y(x),'implicit')
Maple raw output
y(x) = -4*sin(x)+x*cos(x)+1/6*x^3*_C1+1/2*x^2*_C2+_C3*x+_C4