ODE
\[ x \left (1-x^2\right ) y'''(x)+\left (3-8 x^2\right ) y''(x)-14 x y'(x)-4 y(x)=0 \] ODE Classification
[[_3rd_order, _fully, _exact, _linear]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.108507 (sec), leaf count = 50
\[\left \{\left \{y(x)\to \frac {-\frac {c_2}{\sqrt {x^2-1}}-\frac {c_3 \log \left (\sqrt {x^2-1}+x\right )}{\sqrt {x^2-1}}+c_1}{x}\right \}\right \}\]
Maple ✓
cpu = 0.043 (sec), leaf count = 47
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C3}}{x}{\frac {1}{\sqrt {1+x}}}{\frac {1}{\sqrt {x-1}}}}+{\frac {{\it \_C1}}{x}}+{\frac {{\it \_C2}}{x}\ln \left ( x+\sqrt {{x}^{2}-1} \right ) {\frac {1}{\sqrt {{x}^{2}-1}}}} \right \} \] Mathematica raw input
DSolve[-4*y[x] - 14*x*y'[x] + (3 - 8*x^2)*y''[x] + x*(1 - x^2)*y'''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (C[1] - C[2]/Sqrt[-1 + x^2] - (C[3]*Log[x + Sqrt[-1 + x^2]])/Sqrt[-1 + x^2])/x}}
Maple raw input
dsolve(x*(-x^2+1)*diff(diff(diff(y(x),x),x),x)+(-8*x^2+3)*diff(diff(y(x),x),x)-14*x*diff(y(x),x)-4*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = 1/x/(1+x)^(1/2)/(x-1)^(1/2)*_C3+_C1/x+1/x/(x^2-1)^(1/2)*_C2*ln(x+(x^2-1)^(1/2))