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]
\[ \boxed {x y y^{\prime }-\left (x^{2}+1\right ) \left (1-y^{2}\right )=0} \]
✓ 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 {c_{1} {\mathrm e}^{-x^{2}}+x^{2}}}{x} \\ y \left (x \right ) &= -\frac {\sqrt {c_{1} {\mathrm e}^{-x^{2}}+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*}