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

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

[_linear]

Book solution method
Linear ODE

Mathematica ✓
cpu = 0.164677 (sec), leaf count = 54

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

Maple ✓
cpu = 0.024 (sec), leaf count = 47

\[\left [y \left (x \right ) = \frac {\sqrt {\left (x -1\right ) \left (1+x \right )}\, \ln \left (x +\sqrt {x^{2}-1}\right )}{\left (x -1\right ) \left (1+x \right )}+\frac {\textit {\_C1}}{\sqrt {x -1}\, \sqrt {1+x}}\right ]\] Mathematica raw input

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

Mathematica raw output

{{y[x] -> (2*C[1] - Log[1 - x/Sqrt[-1 + x^2]] + Log[1 + x/Sqrt[-1 + x^2]])/(2*Sq
rt[-1 + x^2])}}

Maple raw input

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

Maple raw output

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