4.7.39 $2(x^2+x+1)y^{\prime }(x)=8x^2-(2x+1)y(x)+1$

ODE
$$2(x^2+x+1)y^{\prime }(x)=8x^2-(2x+1)y(x)+1$$ ODE Classification

[_linear]

Book solution method
Linear ODE

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

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

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

$$\{y\left(x\right)=2x-3+\mathit{\_}\mathit{C}\mathit{1}\frac{1}{\sqrt{x^2+x+1}}\}$$ 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