4.1201   y′′(x)− a2y(x) = x + 1

ODE

y′′(x)− a2y(x) = x+ 1

ODE Classification

[[_2nd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica
cpu = 0.147951 (sec), leaf count = 31

{{                            } }
           x-+1-     ax     −ax
   y(x) → − a2  + c1e  + c2e

Maple
cpu = 0.015 (sec), leaf count = 27

{                               }
 y (x ) = eax C2 + e−ax-C1+ − x-− 1
                            a2

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