ODE
\[ y''(x)=a x+b y(x) \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.003564 (sec), leaf count = 38
\[\left \{\left \{y(x)\to -\frac {a x}{b}+c_1 e^{\sqrt {b} x}+c_2 e^{-\sqrt {b} x}\right \}\right \}\]
Maple ✓
cpu = 0.019 (sec), leaf count = 29
\[ \left \{ y \left ( x \right ) ={{\rm e}^{\sqrt {b}x}}{\it \_C2}+{{\rm e}^{-\sqrt {b}x}}{\it \_C1}-{\frac {ax}{b}} \right \} \] Mathematica raw input
DSolve[y''[x] == a*x + b*y[x],y[x],x]
Mathematica raw output
{{y[x] -> -((a*x)/b) + E^(Sqrt[b]*x)*C[1] + C[2]/E^(Sqrt[b]*x)}}
Maple raw input
dsolve(diff(diff(y(x),x),x) = a*x+b*y(x), y(x),'implicit')
Maple raw output
y(x) = exp(b^(1/2)*x)*_C2+exp(-b^(1/2)*x)*_C1-a/b*x