Internal problem ID [3079]
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]
Solve \begin {gather*} \boxed {2 \left (1-x^{2}\right ) y^{\prime }-\sqrt {1-x^{2}}-\left (x +1\right ) y=0} \end {gather*}
✓ 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)
\[ y \relax (x ) = \frac {c_{1}}{\sqrt {x -1}}+\frac {x +1}{\sqrt {-x^{2}+1}} \]
✓ Solution by Mathematica
Time used: 0.295 (sec). Leaf size: 36
DSolve[2(1-x^2)y'[x]==Sqrt[1-x^2]+(1+x)y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2 \sqrt {x+1}+\sqrt {2} c_1}{2 \sqrt {1-x}} \\ \end{align*}