ODE
\[ a^2 y(x)+y''(x)=x^2+x+1 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.149542 (sec), leaf count = 36
\[\left \{\left \{y(x)\to \frac {a^2 \left (x^2+x+1\right )-2}{a^4}+c_1 \cos (a x)+c_2 \sin (a x)\right \}\right \}\]
Maple ✓
cpu = 0.027 (sec), leaf count = 33
\[\left [y \left (x \right ) = \sin \left (a x \right ) \textit {\_C2} +\cos \left (a x \right ) \textit {\_C1} +\frac {-2+\left (x^{2}+x +1\right ) a^{2}}{a^{4}}\right ]\] Mathematica raw input
DSolve[a^2*y[x] + y''[x] == 1 + x + x^2,y[x],x]
Mathematica raw output
{{y[x] -> (-2 + a^2*(1 + x + x^2))/a^4 + C[1]*Cos[a*x] + C[2]*Sin[a*x]}}
Maple raw input
dsolve(diff(diff(y(x),x),x)+a^2*y(x) = x^2+x+1, y(x))
Maple raw output
[y(x) = sin(a*x)*_C2+cos(a*x)*_C1+(-2+(x^2+x+1)*a^2)/a^4]