44.5.14 problem 14

Internal problem ID [7076]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 14
Date solved : Monday, January 27, 2025 at 02:47:12 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 22

dsolve(x*sqrt(1+y(x)^2)=y(x)*sqrt(1+x^2)*diff(y(x),x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.277 (sec). Leaf size: 75

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