Internal problem ID [4165]
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)]`]]
\[ \boxed {x \left (-x^{2}+1\right ) {y^{\prime }}^{2}-2 \left (-x^{2}+1\right ) y y^{\prime }+x \left (1-y^{2}\right )=0} \]
✓ Solution by Maple
Time used: 0.407 (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 \left (x \right ) &= -x \\ y \left (x \right ) &= x \\ y \left (x \right ) &= \sqrt {-c_{1}^{2}+1}+\sqrt {x^{2}-1}\, c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.752 (sec). Leaf size: 75
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 \tan ^{-1}\left (\sqrt {\frac {x-1}{x+1}}\right )+i c_1\right ) \\ y(x)\to -x \cos \left (2 \tan ^{-1}\left (\sqrt {\frac {x-1}{x+1}}\right )-i c_1\right ) \\ y(x)\to -x \\ y(x)\to x \\ \end{align*}