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

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

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.00505317 (sec), leaf count = 13

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

Maple
cpu = 0.005 (sec), leaf count = 13

\[ \left \{ y \relax (x ) ={\it \_C1}\,{x}^{2}-{\it \_C1} \right \} \] Mathematica raw input

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

Mathematica raw output

{{y[x] -> (-1 + x^2)*C[1]}}

Maple raw input

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

Maple raw output

y(x) = _C1*x^2-_C1