ODE
\[ y'''(x)=\sin ^3(x) \] ODE Classification
[[_3rd_order, _quadrature]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0335125 (sec), leaf count = 32
\[\left \{\left \{y(x)\to c_3 x^2+c_2 x+c_1+\frac {3 \cos (x)}{4}-\frac {1}{108} \cos (3 x)\right \}\right \}\]
Maple ✓
cpu = 0.253 (sec), leaf count = 25
\[ \left \{ y \left ( x \right ) ={\frac {3\,\cos \left ( x \right ) }{4}}-{\frac {\cos \left ( 3\,x \right ) }{108}}+{\frac {{\it \_C1}\,{x}^{2}}{2}}+{\it \_C2}\,x+{\it \_C3} \right \} \] Mathematica raw input
DSolve[y'''[x] == Sin[x]^3,y[x],x]
Mathematica raw output
{{y[x] -> C[1] + x*C[2] + x^2*C[3] + (3*Cos[x])/4 - Cos[3*x]/108}}
Maple raw input
dsolve(diff(diff(diff(y(x),x),x),x) = sin(x)^3, y(x),'implicit')
Maple raw output
y(x) = 3/4*cos(x)-1/108*cos(3*x)+1/2*_C1*x^2+_C2*x+_C3