Internal problem ID [14977]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 4. Equations with variables separable and equations reducible to them. Exercises
page 38
Problem number: 50.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x \sqrt {1+y^{2}}+y y^{\prime } \sqrt {x^{2}+1}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(x*sqrt(1+y(x)^2)+y(x)*diff(y(x),x)*sqrt(1+x^2)=0,y(x), singsol=all)
\[ \sqrt {x^{2}+1}+\sqrt {1+y \left (x \right )^{2}}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.29 (sec). Leaf size: 75
DSolve[x*Sqrt[1+y[x]^2]+y[x]*y'[x]*Sqrt[1+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*}