4.7.39 \(2 \left (x^2+x+1\right ) y'(x)=8 x^2-(2 x+1) y(x)+1\)

ODE
\[ 2 \left (x^2+x+1\right ) y'(x)=8 x^2-(2 x+1) y(x)+1 \] ODE Classification

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.024688 (sec), leaf count = 23

\[\left \{\left \{y(x)\to \frac {c_1}{\sqrt {x^2+x+1}}+2 x-3\right \}\right \}\]

Maple
cpu = 0.013 (sec), leaf count = 19

\[ \left \{ y \relax (x ) =2\,x-3+{{\it \_C1}{\frac {1}{\sqrt {{x}^{2}+x+1}}}} \right \} \] Mathematica raw input

DSolve[2*(1 + x + x^2)*y'[x] == 1 + 8*x^2 - (1 + 2*x)*y[x],y[x],x]

Mathematica raw output

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

Maple raw input

dsolve(2*(x^2+x+1)*diff(y(x),x) = 1+8*x^2-(1+2*x)*y(x), y(x),'implicit')

Maple raw output

y(x) = 2*x-3+1/(x^2+x+1)^(1/2)*_C1