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 = 0.189068 (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 = 0.05 (sec), leaf count = 35
\[\left [y \left (x \right ) = \frac {x \left (x^{2}-3\right ) \textit {\_C1}}{\left (x -1\right )^{2} \left (x +1\right )^{2}}+\frac {\textit {\_C2}}{\left (x -1\right )^{2} \left (x +1\right )^{2}}\right ]\] 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))
Maple raw output
[y(x) = x*(x^2-3)/(x-1)^2/(x+1)^2*_C1+1/(x-1)^2/(x+1)^2*_C2]