Internal problem ID [2167]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page
79
Problem number: Problem 20.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {y y^{\prime }+x -\sqrt {x^{2}+y^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 28
dsolve(y(x)*diff(y(x),x)=sqrt(x^2+y(x)^2)-x,y(x), singsol=all)
\[ -c_{1}+\frac {\sqrt {x^{2}+y \relax (x )^{2}}}{y \relax (x )^{2}}+\frac {x}{y \relax (x )^{2}} = 0 \]
✓ Solution by Mathematica
Time used: 0.407 (sec). Leaf size: 57
DSolve[y[x]*y'[x]==Sqrt[x^2+y[x]^2]-x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -e^{\frac {c_1}{2}} \sqrt {2 x+e^{c_1}} \\ y(x)\to e^{\frac {c_1}{2}} \sqrt {2 x+e^{c_1}} \\ y(x)\to 0 \\ \end{align*}