75.4.5 problem 50

Internal problem ID [16707]
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
Date solved : Tuesday, January 28, 2025 at 09:18:56 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.002 (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)
 

\[ \sqrt {x^{2}+1}+\sqrt {1+y^{2}}+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.279 (sec). Leaf size: 75

DSolve[x*Sqrt[1+y[x]^2]+y[x]*D[y[x],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*}