ODE
\[ \left (1-x^2\right ) y''(x)+x y'(x)+3 y(x)=0 \] ODE Classification
[[_2nd_order, _exact, _linear, _homogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.165299 (sec), leaf count = 58
\[\left \{\left \{y(x)\to \left (x^2-1\right )^{3/4} \left (c_2 Q_{\frac {3}{2}}^{\frac {3}{2}}(x)+\frac {\sqrt {\frac {2}{\pi }} c_1 x \left (2 x^2-3\right )}{\left (1-x^2\right )^{3/4}}\right )\right \}\right \}\]
Maple ✓
cpu = 0.052 (sec), leaf count = 27
\[\left [y \left (x \right ) = x \left (2 x^{2}-3\right ) \textit {\_C1} +\textit {\_C2} \left (x -1\right )^{\frac {3}{2}} \left (x +1\right )^{\frac {3}{2}}\right ]\] Mathematica raw input
DSolve[3*y[x] + x*y'[x] + (1 - x^2)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (-1 + x^2)^(3/4)*((Sqrt[2/Pi]*x*(-3 + 2*x^2)*C[1])/(1 - x^2)^(3/4) + C[2]*LegendreQ[3/2, 3/2, x])}}
Maple raw input
dsolve((-x^2+1)*diff(diff(y(x),x),x)+x*diff(y(x),x)+3*y(x) = 0, y(x))
Maple raw output
[y(x) = x*(2*x^2-3)*_C1+_C2*(x-1)^(3/2)*(x+1)^(3/2)]