Internal problem ID [3315]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 20
Problem number: 573.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (x^{2}+1\right ) y y^{\prime }+x \left (1-y^{2}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 29
dsolve((x^2+1)*y(x)*diff(y(x),x)+x*(1-y(x)^2) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {c_{1} x^{2}+c_{1}+1} \\ y \relax (x ) = -\sqrt {c_{1} x^{2}+c_{1}+1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.959 (sec). Leaf size: 57
DSolve[(1+x^2)y[x] y'[x]+x(1-y[x]^2)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {1+e^{2 c_1} \left (x^2+1\right )} \\ y(x)\to \sqrt {1+e^{2 c_1} \left (x^2+1\right )} \\ y(x)\to -1 \\ y(x)\to 1 \\ \end{align*}