Internal problem ID [3143]
Book: An introduction to the solution and applications of differential equations, J.W. Searl,
1966
Section: Chapter 4, Ex. 4.2
Problem number: 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\sqrt {x^{2}+1}\, y^{\prime }+\sqrt {y^{2}+1}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 11
dsolve(sqrt(1+x^2)*diff(y(x),x)+sqrt(1+y(x)^2)=0,y(x), singsol=all)
\[ y \left (x \right ) = -\sinh \left (\operatorname {arcsinh}\left (x \right )+c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.349 (sec). Leaf size: 59
DSolve[Sqrt[1+x^2]*y'[x]+Sqrt[1+y[x]^2]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} e^{-c_1} \left (\left (-1+e^{2 c_1}\right ) \sqrt {x^2+1}-\left (1+e^{2 c_1}\right ) x\right ) \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}