28.1.42 problem 43

Internal problem ID [4348]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 43
Date solved : Monday, January 27, 2025 at 09:07:38 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} y \sqrt {1+y^{2}}+\left (x \sqrt {1+y^{2}}-y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 26

dsolve((y(x)*sqrt(1+y(x)^2))+(x*sqrt(1+y(x)^2)-y(x))*diff(y(x),x)=0,y(x), singsol=all)
 

\[ \frac {x y \left (x \right )-\sqrt {y \left (x \right )^{2}+1}-c_{1}}{y \left (x \right )} = 0 \]

✓ Solution by Mathematica

Time used: 0.444 (sec). Leaf size: 82

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

\begin{align*} y(x)\to \frac {c_1 x-\sqrt {x^2-1+c_1{}^2}}{x^2-1} \\ y(x)\to \frac {\sqrt {x^2-1+c_1{}^2}+c_1 x}{x^2-1} \\ y(x)\to 0 \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}