ODE
\[ \left (1-x^2\right ) y''(x)-6 x y'(x)-4 y(x)=0 \] ODE Classification
[[_2nd_order, _exact, _linear, _homogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0407649 (sec), leaf count = 44
\[\left \{\left \{y(x)\to \frac {3 c_1-c_2 x \left (x^2-3\right )}{3 \sqrt {1-x^2} \left (x^2-1\right )^{3/2}}\right \}\right \}\]
Maple ✓
cpu = 0.012 (sec), leaf count = 26
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}\,{x}^{3}-3\,{\it \_C1}\,x+{\it \_C2}}{ \left ( -1+x \right ) ^{2} \left ( 1+x \right ) ^{2}}} \right \} \] Mathematica raw input
DSolve[-4*y[x] - 6*x*y'[x] + (1 - x^2)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (3*C[1] - x*(-3 + x^2)*C[2])/(3*Sqrt[1 - x^2]*(-1 + x^2)^(3/2))}}
Maple raw input
dsolve((-x^2+1)*diff(diff(y(x),x),x)-6*x*diff(y(x),x)-4*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = (_C1*x^3-3*_C1*x+_C2)/(-1+x)^2/(1+x)^2