ODE
\[ x^4 y''(x)-\left (2 x^2+1\right ) y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.243703 (sec), leaf count = 35
\[\left \{\left \{y(x)\to c_1 e^{\frac {1}{x}} (x-1) x-\frac {1}{2} c_2 e^{-1/x} x (x+1)\right \}\right \}\]
Maple ✓
cpu = 0.081 (sec), leaf count = 27
\[\left [y \left (x \right ) = \textit {\_C1} x \,{\mathrm e}^{\frac {1}{x}} \left (x -1\right )+\textit {\_C2} x \,{\mathrm e}^{-\frac {1}{x}} \left (x +1\right )\right ]\] Mathematica raw input
DSolve[-((1 + 2*x^2)*y[x]) + x^4*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> E^x^(-1)*(-1 + x)*x*C[1] - (x*(1 + x)*C[2])/(2*E^x^(-1))}}
Maple raw input
dsolve(x^4*diff(diff(y(x),x),x)-(2*x^2+1)*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*x*exp(1/x)*(x-1)+_C2*x*exp(-1/x)*(x+1)]