Internal problem ID [2676]
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]
\[ \boxed {y^{\prime } y-\sqrt {y^{2}+x^{2}}=-x} \]
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 28
dsolve(y(x)*diff(y(x),x)=sqrt(x^2+y(x)^2)-x,y(x), singsol=all)
\[ -c_{1} +\frac {\sqrt {x^{2}+y \left (x \right )^{2}}}{y \left (x \right )^{2}}+\frac {x}{y \left (x \right )^{2}} = 0 \]
✓ Solution by Mathematica
Time used: 0.409 (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*}