ODE
\[ y''(x)+y(x)=a x \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.00327922 (sec), leaf count = 19
\[\left \{\left \{y(x)\to a x+c_2 \sin (x)+c_1 \cos (x)\right \}\right \}\]
Maple ✓
cpu = 0.204 (sec), leaf count = 16
\[ \left \{ y \left ( x \right ) =\sin \left ( x \right ) {\it \_C2}+\cos \left ( x \right ) {\it \_C1}+ax \right \} \] 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),'implicit')
Maple raw output
y(x) = sin(x)*_C2+cos(x)*_C1+a*x