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 = 0.184761 (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 = 0.319 (sec), leaf count = 29
\[\left [y \left (x \right ) = -\frac {\mathit {c1} \cos \left (a x \right )}{a^{2}}-\frac {\mathit {c2} \sin \left (b x \right )}{b^{2}}+\textit {\_C1} x +\textit {\_C2}\right ]\] 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))
Maple raw output
[y(x) = -c1/a^2*cos(a*x)-c2/b^2*sin(b*x)+_C1*x+_C2]