27.2.4 problem 4

Internal problem ID [4304]
Book : An introduction to the solution and applications of differential equations, J.W. Searl, 1966
Section : Chapter 4, Ex. 4.2
Problem number : 4
Date solved : Monday, January 27, 2025 at 09:00:46 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (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: 0.195 (sec). Leaf size: 29

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

\begin{align*} y(x)\to -\sinh (\text {arcsinh}(x)-c_1) \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}