4.31.24 \(\left (1-x^2\right ) y''(x)-x y'(x)+y(x)=0\)

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

[[_2nd_order, _exact, _linear, _homogeneous]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.217329 (sec), leaf count = 63

\[\left \{\left \{y(x)\to c_1 \cosh \left (\frac {\sqrt {1-x^2} \sin ^{-1}(x)}{\sqrt {x^2-1}}\right )+i c_2 \sinh \left (\frac {\sqrt {1-x^2} \sin ^{-1}(x)}{\sqrt {x^2-1}}\right )\right \}\right \}\]

Maple ✓
cpu = 0.049 (sec), leaf count = 20

\[\left [y \left (x \right ) = \textit {\_C1} x +\textit {\_C2} \sqrt {x -1}\, \sqrt {x +1}\right ]\] Mathematica raw input

DSolve[y[x] - x*y'[x] + (1 - x^2)*y''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> C[1]*Cosh[(Sqrt[1 - x^2]*ArcSin[x])/Sqrt[-1 + x^2]] + I*C[2]*Sinh[(Sqr
t[1 - x^2]*ArcSin[x])/Sqrt[-1 + x^2]]}}

Maple raw input

dsolve((-x^2+1)*diff(diff(y(x),x),x)-x*diff(y(x),x)+y(x) = 0, y(x))

Maple raw output

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