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 = 0.0364807 (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 = 0.061 (sec), leaf count = 27
\[ \left \{ y \left ( x \right ) = \left ( {\it \_C2}\, \left ( 1+x \right ) {{\rm e}^{-{x}^{-1}}}+{\it \_C1}\,{{\rm e}^{{x}^{-1}}} \left ( -1+x \right ) \right ) x \right \} \] 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),'implicit')
Maple raw output
y(x) = (_C2*(1+x)*exp(-1/x)+_C1*exp(1/x)*(-1+x))*x