ODE
\[ \left (a^2-x^2\right ) y''(x)-8 x y'(x)-12 y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0472978 (sec), leaf count = 38
\[\left \{\left \{y(x)\to \frac {\frac {c_2 \left (a^2+3 x^2\right )}{(a-x)^3}+3 c_1}{3 (a+x)^3}\right \}\right \}\]
Maple ✓
cpu = 0.03 (sec), leaf count = 41
\[ \left \{ y \left ( x \right ) ={\frac {3\,{\it \_C2}\,{a}^{2}x+{\it \_C2}\,{x}^{3}+{\it \_C1}\,{a}^{2}+3\,{\it \_C1}\,{x}^{2}}{ \left ( a-x \right ) ^{3} \left ( a+x \right ) ^{3}}} \right \} \] Mathematica raw input
DSolve[-12*y[x] - 8*x*y'[x] + (a^2 - x^2)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (3*C[1] + ((a^2 + 3*x^2)*C[2])/(a - x)^3)/(3*(a + x)^3)}}
Maple raw input
dsolve((a^2-x^2)*diff(diff(y(x),x),x)-8*x*diff(y(x),x)-12*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = (3*_C2*a^2*x+_C2*x^3+_C1*a^2+3*_C1*x^2)/(a-x)^3/(a+x)^3