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

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

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.0193686 (sec), leaf count = 42

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

Maple
cpu = 0.523 (sec), leaf count = 58

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