Internal problem ID [3920]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 7
Problem number: First order with homogeneous Coefficients. Exercise 7.3, page
61.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {\left (x +\sqrt {y^{2}-y x}\right ) y^{\prime }-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve((x+sqrt(y(x)^2-x*y(x)))*diff(y(x),x)-y(x)=0,y(x), singsol=all)
\[ \ln \left (y \relax (x )\right )+\frac {2 \sqrt {y \relax (x ) \left (-x +y \relax (x )\right )}}{y \relax (x )}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.298 (sec). Leaf size: 43
DSolve[(x+Sqrt[y[x]^2-x*y[x]])*y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {2 \sqrt {\frac {y(x)}{x}-1}}{\sqrt {\frac {y(x)}{x}}}+\log \left (\frac {y(x)}{x}\right )=-\log (x)+c_1,y(x)\right ] \]