ODE
\[ y''(x)+y(x)=a x \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.149393 (sec), leaf count = 19
\[\{\{y(x)\to a x+c_1 \cos (x)+c_2 \sin (x)\}\}\]
Maple ✓
cpu = 0.019 (sec), leaf count = 16
\[[y \left (x \right ) = \sin \left (x \right ) \textit {\_C2} +\textit {\_C1} \cos \left (x \right )+a x]\] Mathematica raw input
DSolve[y[x] + y''[x] == a*x,y[x],x]
Mathematica raw output
{{y[x] -> a*x + C[1]*Cos[x] + C[2]*Sin[x]}}
Maple raw input
dsolve(diff(diff(y(x),x),x)+y(x) = a*x, y(x))
Maple raw output
[y(x) = sin(x)*_C2+_C1*cos(x)+a*x]