ODE
\[ 4 \left (x^2+1\right ) y''(x)=x^2+4 x y'(x) \] ODE Classification
[[_2nd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.224131 (sec), leaf count = 57
\[\left \{\left \{y(x)\to \frac {1}{16} \left (-3 x^2+2 \sqrt {x^2+1} x \sinh ^{-1}(x)+8 c_1 \sqrt {x^2+1} x+\sinh ^{-1}(x)^2+8 c_1 \sinh ^{-1}(x)+16 c_2\right )\right \}\right \}\]
Maple ✓
cpu = 0.449 (sec), leaf count = 47
\[\left [y \left (x \right ) = \textit {\_C1} \left (\frac {x \sqrt {x^{2}+1}}{2}+\frac {\arcsinh \left (x \right )}{2}\right )-\frac {3 x^{2}}{16}+\frac {\arcsinh \left (x \right ) \sqrt {x^{2}+1}\, x}{8}+\frac {\arcsinh \left (x \right )^{2}}{16}-\frac {1}{16}+\textit {\_C2}\right ]\] Mathematica raw input
DSolve[4*(1 + x^2)*y''[x] == x^2 + 4*x*y'[x],y[x],x]
Mathematica raw output
{{y[x] -> (-3*x^2 + 2*x*Sqrt[1 + x^2]*ArcSinh[x] + ArcSinh[x]^2 + 8*x*Sqrt[1 + x^2]*C[1] + 8*ArcSinh[x]*C[1] + 16*C[2])/16}}
Maple raw input
dsolve(4*(x^2+1)*diff(diff(y(x),x),x) = 4*x*diff(y(x),x)+x^2, y(x))
Maple raw output
[y(x) = _C1*(1/2*x*(x^2+1)^(1/2)+1/2*arcsinh(x))-3/16*x^2+1/8*arcsinh(x)*(x^2+1)^(1/2)*x+1/16*arcsinh(x)^2-1/16+_C2]