Internal problem ID [2678]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x)*G(y),0]]]
Solve \begin {gather*} \boxed {y \sqrt {1+y^{2}}+\left (x \sqrt {1+y^{2}}-y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
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)
\[ x -\frac {\sqrt {1+y \relax (x )^{2}}+c_{1}}{y \relax (x )} = 0 \]
✓ Solution by Mathematica
Time used: 0.471 (sec). Leaf size: 82
DSolve[(y[x]*Sqrt[1+y[x]^2])+(x*Sqrt[1+y[x]^2]-y[x])*y'[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*}