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

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

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.0132908 (sec), leaf count = 43

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

Maple
cpu = 0.013 (sec), leaf count = 53

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

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

Mathematica raw output

{{y[x] -> -x + Sqrt[-1 + x^2]*C[1] + Sqrt[-1 + x^2]*Log[x + Sqrt[-1 + x^2]]}}

Maple raw input

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

Maple raw output

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