4.7.40 $4(x^2+1)y^{\prime }(x)-x^2-4xy(x)=0$

ODE
$$4(x^2+1)y^{\prime }(x)-x^2-4xy(x)=0$$ ODE Classification

[_linear]

Book solution method
Linear ODE

Mathematica ✓
cpu = 0.0230519 (sec), leaf count = 38

$$\left\{\{y(x)\to \frac{1}{4}(4c_1\sqrt{x^2+1}+\sqrt{x^2+1}{\sinh }^{-1}(x)-x)\}\right\}$$

Maple ✓
cpu = 0.016 (sec), leaf count = 23

$$\{y\left(x\right)=\frac{4\mathit{\_}\mathit{C}\mathit{1}+\mathit{A}\mathit{r}\mathit{c}\mathit{s}\mathit{i}\mathit{n}\mathit{h}\left(x\right)}{4}\sqrt{x^2+1}-\frac{x}{4}\}$$ Mathematica raw input

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

Mathematica raw output

{{y[x] -> (-x + Sqrt[1 + x^2]*ArcSinh[x] + 4*Sqrt[1 + x^2]*C[1])/4}}

Maple raw input

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

Maple raw output

y(x) = 1/4*(4*_C1+arcsinh(x))*(x^2+1)^(1/2)-1/4*x