ODE
\[ \left (1-a^2 x^2\right ) y''(x)-2 a^2 x y'(x)=0 \] ODE Classification
[[_2nd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.183293 (sec), leaf count = 19
\[\left \{\left \{y(x)\to c_2-\frac {c_1 \tanh ^{-1}(a x)}{a}\right \}\right \}\]
Maple ✓
cpu = 0.052 (sec), leaf count = 31
\[\left [y \left (x \right ) = \textit {\_C1} +\left (\frac {\ln \left (a x -1\right )}{2 a}-\frac {\ln \left (a x +1\right )}{2 a}\right ) \textit {\_C2}\right ]\] Mathematica raw input
DSolve[-2*a^2*x*y'[x] + (1 - a^2*x^2)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -((ArcTanh[a*x]*C[1])/a) + C[2]}}
Maple raw input
dsolve((-a^2*x^2+1)*diff(diff(y(x),x),x)-2*a^2*x*diff(y(x),x) = 0, y(x))
Maple raw output
[y(x) = _C1+(1/2/a*ln(a*x-1)-1/2/a*ln(a*x+1))*_C2]