4.7.34 \(2 \left (1-x^2\right ) y'(x)=\sqrt {1-x^2}+(x+1) y(x)\)

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 = 0.036943 (sec), leaf count = 33

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

Maple
cpu = 0.013 (sec), leaf count = 25

\[ \left \{ y \relax (x ) ={{\it \_C1}{\frac {1}{\sqrt {-1+x}}}}+{(1+x){\frac {1}{\sqrt {-{x}^{2}+1}}}} \right \} \] 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),'implicit')

Maple raw output

y(x) = 1/(-1+x)^(1/2)*_C1+(1+x)/(-x^2+1)^(1/2)