Internal problem ID [3187]
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]`]]
\[ \boxed {y \sqrt {y^{2}+1}+\left (x \sqrt {y^{2}+1}-y\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (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: 0.479 (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*}