4.36.10 \(x^6 y''(x)+3 x^5 y'(x)+y(x)=0\)

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)