ODE
\[ 4 x^3 y'''(x)+x y'(x)-y(x)=0 \] ODE Classification
[[_3rd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0133121 (sec), leaf count = 38
\[\left \{\left \{y(x)\to x \left (c_1 x^{-\frac {\sqrt {3}}{2}}+c_2 x^{\frac {\sqrt {3}}{2}}+c_3\right )\right \}\right \}\]
Maple ✓
cpu = 0.007 (sec), leaf count = 30
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,x+{\it \_C2}\,{x}^{1+{\frac {\sqrt {3}}{2}}}+{\it \_C3}\,{x}^{1-{\frac {\sqrt {3}}{2}}} \right \} \] Mathematica raw input
DSolve[-y[x] + x*y'[x] + 4*x^3*y'''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> x*(C[1]/x^(Sqrt[3]/2) + x^(Sqrt[3]/2)*C[2] + C[3])}}
Maple raw input
dsolve(4*x^3*diff(diff(diff(y(x),x),x),x)+x*diff(y(x),x)-y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = _C1*x+_C2*x^(1+1/2*3^(1/2))+_C3*x^(1-1/2*3^(1/2))