Internal problem ID [3766]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 19
Problem number: 514.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y y^{\prime } x -\left (x^{2}+1\right ) \left (1-y^{2}\right )=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 44
dsolve(x*y(x)*diff(y(x),x) = (x^2+1)*(1-y(x)^2),y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {\sqrt {{\mathrm e}^{-x^{2}} c_{1} +x^{2}}}{x} y \left (x \right ) = -\frac {\sqrt {{\mathrm e}^{-x^{2}} c_{1} +x^{2}}}{x} \end{align*}
✓ Solution by Mathematica
Time used: 5.562 (sec). Leaf size: 99
DSolve[x y[x] y'[x]==(1+x^2)(1-y[x]^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {x^2+e^{-x^2+2 c_1}}}{x} y(x)\to \frac {\sqrt {x^2+e^{-x^2+2 c_1}}}{x} y(x)\to -1 y(x)\to 1 y(x)\to -\frac {\sqrt {x^2}}{x} y(x)\to \frac {\sqrt {x^2}}{x} \end{align*}