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 = 0.163231 (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 = 0.011 (sec), leaf count = 30
\[\left [y \left (x \right ) = \textit {\_C1} x +\textit {\_C2} \,x^{1+\frac {\sqrt {3}}{2}}+\textit {\_C3} \,x^{1-\frac {\sqrt {3}}{2}}\right ]\] 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))
Maple raw output
[y(x) = _C1*x+_C2*x^(1+1/2*3^(1/2))+_C3*x^(1-1/2*3^(1/2))]