29.19.1 problem 514

Internal problem ID [5110]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 19
Problem number : 514
Date solved : Monday, January 27, 2025 at 10:11:49 AM
CAS classification : [_separable]

\begin{align*} x y y^{\prime }&=\left (x^{2}+1\right ) \left (1-y^{2}\right ) \end{align*}

✓ Solution by Maple

Time used: 0.021 (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: 5.308 (sec). Leaf size: 101

DSolve[x y[x] D[y[x],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+2 c_1}}}{x} \\ y(x)\to \frac {\sqrt {x^2+e^{-x^2-2+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*}