4.28.9 \(4 x^3 y(x)+x y''(x)-y'(x)=0\)

ODE
\[ 4 x^3 y(x)+x y''(x)-y'(x)=0 \] ODE Classification

[[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

Book solution method
TO DO

Mathematica
cpu = 0.0452003 (sec), leaf count = 20

\[\left \{\left \{y(x)\to c_2 \sin \left (x^2\right )+c_1 \cos \left (x^2\right )\right \}\right \}\]

Maple
cpu = 0.007 (sec), leaf count = 17

\[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sin \left ( {x}^{2} \right ) +{\it \_C2}\,\cos \left ( {x}^{2} \right ) \right \} \] Mathematica raw input

DSolve[4*x^3*y[x] - y'[x] + x*y''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> C[1]*Cos[x^2] + C[2]*Sin[x^2]}}

Maple raw input

dsolve(x*diff(diff(y(x),x),x)-diff(y(x),x)+4*x^3*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = _C1*sin(x^2)+_C2*cos(x^2)