Internal problem ID [3333]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 21
Problem number: 591.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y y^{\prime } \sqrt {x^{2}+1}+x \sqrt {1+y^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (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)
\[ \sqrt {x^{2}+1}+\sqrt {1+y \relax (x )^{2}}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.264 (sec). Leaf size: 75
DSolve[y[x] y'[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*}