ODE
\[ y''(x)=\text {c1} \cos (a x)+\text {c2} \sin (b x) \] ODE Classification
[[_2nd_order, _quadrature]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0399112 (sec), leaf count = 32
\[\left \{\left \{y(x)\to -\frac {\text {c1} \cos (a x)}{a^2}-\frac {\text {c2} \sin (b x)}{b^2}+c_2 x+c_1\right \}\right \}\]
Maple ✓
cpu = 0.029 (sec), leaf count = 29
\[ \left \{ y \left ( x \right ) =-{\frac {{\it c1}\,\cos \left ( ax \right ) }{{a}^{2}}}-{\frac {{\it c2}\,\sin \left ( bx \right ) }{{b}^{2}}}+{\it \_C1}\,x+{\it \_C2} \right \} \] Mathematica raw input
DSolve[y''[x] == c1*Cos[a*x] + c2*Sin[b*x],y[x],x]
Mathematica raw output
{{y[x] -> C[1] + x*C[2] - (c1*Cos[a*x])/a^2 - (c2*Sin[b*x])/b^2}}
Maple raw input
dsolve(diff(diff(y(x),x),x) = c1*cos(a*x)+c2*sin(b*x), y(x),'implicit')
Maple raw output
y(x) = -c1/a^2*cos(a*x)-c2/b^2*sin(b*x)+_C1*x+_C2