ODE
\[ x^6 y''(x)+3 x^5 y'(x)+y(x)=0 \] ODE Classification
[[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0176002 (sec), leaf count = 29
\[\left \{\left \{y(x)\to c_1 \cos \left (\frac {1}{2 x^2}\right )-c_2 \sin \left (\frac {1}{2 x^2}\right )\right \}\right \}\]
Maple ✓
cpu = 0.008 (sec), leaf count = 21
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sin \left ( {\frac {1}{2\,{x}^{2}}} \right ) +{\it \_C2}\,\cos \left ( {\frac {1}{2\,{x}^{2}}} \right ) \right \} \] Mathematica raw input
DSolve[y[x] + 3*x^5*y'[x] + x^6*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1]*Cos[1/(2*x^2)] - C[2]*Sin[1/(2*x^2)]}}
Maple raw input
dsolve(x^6*diff(diff(y(x),x),x)+3*x^5*diff(y(x),x)+y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = _C1*sin(1/2/x^2)+_C2*cos(1/2/x^2)