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 = 0.160336 (sec), leaf count = 20
\[\left \{\left \{y(x)\to c_1 \cos \left (x^2\right )+c_2 \sin \left (x^2\right )\right \}\right \}\]
Maple ✓
cpu = 0.037 (sec), leaf count = 17
\[[y \left (x \right ) = \textit {\_C1} \sin \left (x^{2}\right )+\textit {\_C2} \cos \left (x^{2}\right )]\] 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))
Maple raw output
[y(x) = _C1*sin(x^2)+_C2*cos(x^2)]