29.18.27 problem 505

Internal problem ID [5101]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 18
Problem number : 505
Date solved : Monday, January 27, 2025 at 10:11:18 AM
CAS classification : [_separable]

\begin{align*} x y y^{\prime }+1+y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 34

dsolve(x*y(x)*diff(y(x),x)+1+y(x)^2 = 0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.344 (sec). Leaf size: 96

DSolve[x y[x] D[y[x],x]+1+y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {\sqrt {-x^2+e^{2 c_1}}}{x} \\ y(x)\to \frac {\sqrt {-x^2+e^{2 c_1}}}{x} \\ y(x)\to -i \\ y(x)\to i \\ y(x)\to \frac {x}{\sqrt {-x^2}} \\ y(x)\to \frac {\sqrt {-x^2}}{x} \\ \end{align*}