4.1598   (x2 + 3x+ 4)y′′(x)+ (x2 +x + 1)y′(x) − (2x + 3)y(x) = 0

ODE

(x2 + 3x+ 4)y′′(x)+ (x2 +x + 1)y′(x) − (2x + 3)y(x) = 0

ODE Classification

[[_2nd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica
cpu = 0.0566449 (sec), leaf count = 23

{{y (x) → c2(x2 + x + 3)+ c1e− x} }

Maple
cpu = 0.044 (sec), leaf count = 19

{y(x) = C1e −x +-C2 (x2 + x+ 3)}

Mathematica raw input

DSolve[-((3 + 2*x)*y[x]) + (1 + x + x^2)*y'[x] + (4 + 3*x + x^2)*y''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> C[1]/E^x + (3 + x + x^2)*C[2]}}

Maple raw input

dsolve((x^2+3*x+4)*diff(diff(y(x),x),x)+(x^2+x+1)*diff(y(x),x)-(3+2*x)*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = _C1*exp(-x)+_C2*(x^2+x+3)