ODE
\[ x^3 y'''(x)+\left (1-a^2\right ) x y'(x)+3 x^2 y''(x)=0 \] ODE Classification
[[_3rd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0417486 (sec), leaf count = 29
\[\left \{\left \{y(x)\to \frac {-c_1 x^{-a}+c_2 x^a+a c_3}{a}\right \}\right \}\]
Maple ✓
cpu = 0.012 (sec), leaf count = 18
\[ \left \{ y \left ( x \right ) ={\it \_C1}+{\it \_C2}\,{x}^{a}+{\it \_C3}\,{x}^{-a} \right \} \] Mathematica raw input
DSolve[(1 - a^2)*x*y'[x] + 3*x^2*y''[x] + x^3*y'''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (-(C[1]/x^a) + x^a*C[2] + a*C[3])/a}}
Maple raw input
dsolve(x^3*diff(diff(diff(y(x),x),x),x)+3*x^2*diff(diff(y(x),x),x)+(-a^2+1)*x*diff(y(x),x) = 0, y(x),'implicit')
Maple raw output
y(x) = _C1+_C2*x^a+_C3*x^(-a)