ODE
\[ x \left (1-x^2\right ) y'(x)=\left (1-2 x^2\right ) y(x)+\left (1-x^2\right ) x^3 \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.172943 (sec), leaf count = 26
\[\left \{\left \{y(x)\to x \left (x^2+c_1 \sqrt {1-x^2}-1\right )\right \}\right \}\]
Maple ✓
cpu = 0.01 (sec), leaf count = 26
\[\left [y \left (x \right ) = x \left (x -1\right ) \left (1+x \right )+x \sqrt {1+x}\, \sqrt {x -1}\, \textit {\_C1}\right ]\] Mathematica raw input
DSolve[x*(1 - x^2)*y'[x] == x^3*(1 - x^2) + (1 - 2*x^2)*y[x],y[x],x]
Mathematica raw output
{{y[x] -> x*(-1 + x^2 + Sqrt[1 - x^2]*C[1])}}
Maple raw input
dsolve(x*(-x^2+1)*diff(y(x),x) = x^3*(-x^2+1)+(-2*x^2+1)*y(x), y(x))
Maple raw output
[y(x) = x*(x-1)*(1+x)+x*(1+x)^(1/2)*(x-1)^(1/2)*_C1]