4.44.47 \(x \left (1-x^2\right ) y'''(x)+\left (3-8 x^2\right ) y''(x)-14 x y'(x)-4 y(x)=0\)

ODE
\[ x \left (1-x^2\right ) y'''(x)+\left (3-8 x^2\right ) y''(x)-14 x y'(x)-4 y(x)=0 \] ODE Classification

[[_3rd_order, _fully, _exact, _linear]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.268001 (sec), leaf count = 63

\[\left \{\left \{y(x)\to \frac {-\frac {c_2}{\sqrt {x^2-1}}+\frac {1}{2} c_3 \left (\frac {2 \sin ^{-1}(x)}{\sqrt {1-x^2}}-\log (1-x)+\log (x+1)-2 \tanh ^{-1}(x)\right )+c_1}{x}\right \}\right \}\]

Maple ✓
cpu = 0.174 (sec), leaf count = 47

\[\left [y \left (x \right ) = \frac {\textit {\_C3}}{x \sqrt {x +1}\, \sqrt {x -1}}+\frac {\textit {\_C1}}{x}+\frac {\textit {\_C2} \ln \left (x +\sqrt {x^{2}-1}\right )}{x \sqrt {x^{2}-1}}\right ]\] 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]*((2*ArcSin[x])/Sqrt[1 - x^2] - 2*A
rcTanh[x] - Log[1 - x] + Log[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))

Maple raw output

[y(x) = 1/x/(x+1)^(1/2)/(x-1)^(1/2)*_C3+1/x*_C1+1/x/(x^2-1)^(1/2)*_C2*ln(x+(x^2-
1)^(1/2))]