Internal problem ID [2677]
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: 42.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _dAlembert]
Solve \begin {gather*} \boxed {x -\sqrt {x^{2}+y^{2}}+\left (y-\sqrt {x^{2}+y^{2}}\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.019 (sec). Leaf size: 58
dsolve((x-sqrt(x^2+y(x)^2))+(y(x)-sqrt(x^2+y(x)^2))*diff(y(x),x)=0,y(x), singsol=all)
\[ -c_{1}+\frac {\sqrt {x^{2}+y \relax (x )^{2}}}{x^{2} y \relax (x )}+\frac {1}{x y \relax (x )}+\frac {1}{y \relax (x )^{2}}+\frac {1}{x^{2}}+\frac {\sqrt {x^{2}+y \relax (x )^{2}}}{x y \relax (x )^{2}} = 0 \]
✓ Solution by Mathematica
Time used: 29.052 (sec). Leaf size: 125
DSolve[(x-Sqrt[x^2+y[x]^2])+(y[x]-Sqrt[x^2+y[x]^2])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{2 c_1} x-\sqrt {2} \sqrt {e^{2 c_1} \left (-x^2+e^{2 c_1}\right ){}^2}}{x^2-2 e^{2 c_1}} \\ y(x)\to \frac {\sqrt {2} \sqrt {e^{2 c_1} \left (-x^2+e^{2 c_1}\right ){}^2}+e^{2 c_1} x}{x^2-2 e^{2 c_1}} \\ y(x)\to 0 \\ \end{align*}