Internal problem ID [5457]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Section 1.7. Homogeneous Equations. Page
28
Problem number: 1(h).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {x y^{\prime }-\sqrt {x^{2}+y^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 49
dsolve(x*diff(y(x),x)=sqrt(x^2+y(x)^2),y(x), singsol=all)
\[ \frac {y \relax (x )^{2}}{x^{2}}+\frac {y \relax (x ) \sqrt {x^{2}+y \relax (x )^{2}}}{x^{2}}+\ln \left (y \relax (x )+\sqrt {x^{2}+y \relax (x )^{2}}\right )-3 \ln \relax (x )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.158 (sec). Leaf size: 62
DSolve[x*y'[x]==Sqrt[x^2+y[x]^2],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{2} \left (\frac {y(x) \left (\sqrt {\frac {y(x)^2}{x^2}+1}+\frac {y(x)}{x}\right )}{x}+\tanh ^{-1}\left (\frac {y(x)}{x \sqrt {\frac {y(x)^2}{x^2}+1}}\right )\right )=\log (x)+c_1,y(x)\right ] \]