4.7.40 \(4 \left (x^2+1\right ) y'(x)-x^2-4 x y(x)=0\)

ODE
\[ 4 \left (x^2+1\right ) y'(x)-x^2-4 x y(x)=0 \] ODE Classification

[_linear]

Book solution method
Linear ODE

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

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

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

\[ \left \{ y \relax (x ) ={\frac {4\,{\it \_C1}+{\it Arcsinh} \relax (x ) }{4}\sqrt {{x}^{2}+1}}-{\frac {x}{4}} \right \} \] 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