ODE
\[ 2 \left (1-x^2\right ) y'(x)=\sqrt {1-x^2}+(x+1) y(x) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.24331 (sec), leaf count = 33
\[\left \{\left \{y(x)\to \frac {x+1}{\sqrt {1-x^2}}+\frac {c_1}{\sqrt {2-2 x}}\right \}\right \}\]
Maple ✓
cpu = 0.012 (sec), leaf count = 25
\[\left [y \left (x \right ) = \frac {\textit {\_C1}}{\sqrt {x -1}}+\frac {1+x}{\sqrt {-x^{2}+1}}\right ]\] Mathematica raw input
DSolve[2*(1 - x^2)*y'[x] == Sqrt[1 - x^2] + (1 + x)*y[x],y[x],x]
Mathematica raw output
{{y[x] -> (1 + x)/Sqrt[1 - x^2] + C[1]/Sqrt[2 - 2*x]}}
Maple raw input
dsolve(2*(-x^2+1)*diff(y(x),x) = (-x^2+1)^(1/2)+(1+x)*y(x), y(x))
Maple raw output
[y(x) = 1/(x-1)^(1/2)*_C1+(1+x)/(-x^2+1)^(1/2)]