29.21.15 problem 591

Internal problem ID [5185]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 21
Problem number : 591
Date solved : Monday, January 27, 2025 at 10:18:23 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 20

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

\[ \sqrt {x^{2}+1}+\sqrt {y \left (x \right )^{2}+1}+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.295 (sec). Leaf size: 75

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

\begin{align*} y(x)\to -\sqrt {x^2+c_1 \left (-2 \sqrt {x^2+1}+c_1\right )} \\ y(x)\to \sqrt {x^2+c_1 \left (-2 \sqrt {x^2+1}+c_1\right )} \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}