ODE
\[ y''(x)-a^2 y(x)=x+1 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.147951 (sec), leaf count = 31
\[\left \{\left \{y(x)\to -\frac {x+1}{a^2}+c_1 e^{a x}+c_2 e^{-a x}\right \}\right \}\]
Maple ✓
cpu = 0.015 (sec), leaf count = 27
\[ \left \{ y \left ( x \right ) ={{\rm e}^{ax}}{\it \_C2}+{{\rm e}^{-ax}}{\it \_C1}+{\frac {-x-1}{{a}^{2}}} \right \} \] Mathematica raw input
DSolve[-(a^2*y[x]) + y''[x] == 1 + x,y[x],x]
Mathematica raw output
{{y[x] -> -((1 + x)/a^2) + E^(a*x)*C[1] + C[2]/E^(a*x)}}
Maple raw input
dsolve(diff(diff(y(x),x),x)-a^2*y(x) = 1+x, y(x),'implicit')
Maple raw output
y(x) = exp(a*x)*_C2+exp(-a*x)*_C1+(-x-1)/a^2