Internal problem ID [3657]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 31
Problem number: 931.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_rational, [_1st_order, _with_symmetry_[F(x),G(x)*y+H(x)]]]
Solve \begin {gather*} \boxed {x \left (1-x^{2}\right ) \left (y^{\prime }\right )^{2}-2 \left (1-x^{2}\right ) y y^{\prime }+x \left (1-y^{2}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.328 (sec). Leaf size: 33
dsolve(x*(-x^2+1)*diff(y(x),x)^2-2*(-x^2+1)*y(x)*diff(y(x),x)+x*(1-y(x)^2) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -x \\ y \relax (x ) = x \\ y \relax (x ) = \sqrt {-c_{1}^{2}+1}+\sqrt {x^{2}-1}\, c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.064 (sec). Leaf size: 73
DSolve[x(1-x^2) (y'[x])^2-2(1-x^2)y[x] y'[x]+x(1-y[x]^2)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \cos \left (2 \text {ArcTan}\left (\sqrt {\frac {x-1}{x+1}}\right )+i c_1\right ) \\ y(x)\to x \cos \left (2 \text {ArcTan}\left (\sqrt {\frac {x-1}{x+1}}\right )-i c_1\right ) \\ y(x)\to -x \\ y(x)\to x \\ \end{align*}