Internal problem ID [2170]
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 23.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {x \sqrt {x^{2}+y^{2}}+y^{2}}{y x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 24
dsolve(diff(y(x),x)=(x*sqrt(y(x)^2+x^2)+y(x)^2)/(x*y(x)),y(x), singsol=all)
\[ -\frac {\sqrt {x^{2}+y \relax (x )^{2}}}{x}+\ln \relax (x )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.252 (sec). Leaf size: 48
DSolve[y'[x]==(x*Sqrt[y[x]^2+x^2]+y[x]^2)/(x*y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x \sqrt {(\log (x)-1+c_1) (\log (x)+1+c_1)} \\ y(x)\to x \sqrt {(\log (x)-1+c_1) (\log (x)+1+c_1)} \\ \end{align*}