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 = 0.176148 (sec), leaf count = 38
\[\left \{\left \{y(x)\to \frac {1}{4} \left (\sqrt {x^2+1} \sinh ^{-1}(x)+4 c_1 \sqrt {x^2+1}-x\right )\right \}\right \}\]
Maple ✓
cpu = 0.014 (sec), leaf count = 28
\[\left [y \left (x \right ) = \left (-\frac {x}{4 \sqrt {x^{2}+1}}+\frac {\arcsinh \left (x \right )}{4}+\textit {\_C1} \right ) \sqrt {x^{2}+1}\right ]\] 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))
Maple raw output
[y(x) = (-1/4*x/(x^2+1)^(1/2)+1/4*arcsinh(x)+_C1)*(x^2+1)^(1/2)]