Internal problem ID [3587]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 12
Problem number: 331.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {2 \left (-x^{2}+1\right ) y^{\prime }-\left (x +1\right ) y=\sqrt {-x^{2}+1}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(2*(-x^2+1)*diff(y(x),x) = sqrt(-x^2+1)+(1+x)*y(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1}}{\sqrt {x -1}}+\frac {x +1}{\sqrt {-x^{2}+1}} \]
✓ Solution by Mathematica
Time used: 0.34 (sec). Leaf size: 40
DSolve[2(1-x^2)y'[x]==Sqrt[1-x^2]+(1+x)y[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {2 \sqrt {1-x^2}+c_1 \sqrt {2-2 x}}{2 (x-1)} \]