ODE
\[ \left (1-x^2\right ) y'(x)+x^2+x y(x)=0 \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.171737 (sec), leaf count = 35
\[\left \{\left \{y(x)\to \sqrt {1-x^2} \sin ^{-1}(x)+c_1 \sqrt {x^2-1}-x\right \}\right \}\]
Maple ✓
cpu = 0.012 (sec), leaf count = 60
\[\left [y \left (x \right ) = \frac {\ln \left (x +\sqrt {x^{2}-1}\right ) x^{2}}{\sqrt {x^{2}-1}}-x -\frac {\ln \left (x +\sqrt {x^{2}-1}\right )}{\sqrt {x^{2}-1}}+\sqrt {x -1}\, \sqrt {1+x}\, \textit {\_C1}\right ]\] 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]*ArcSin[x] + Sqrt[-1 + x^2]*C[1]}}
Maple raw input
dsolve((-x^2+1)*diff(y(x),x)+x^2+x*y(x) = 0, y(x))
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))+(x-1)^(1/2)*(1+x)^(1/2)*_C1]