Internal problem ID [3924]
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 7.7, page
61.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _dAlembert]
Solve \begin {gather*} \boxed {y^{2}+\left (x \sqrt {y^{2}-x^{2}}-y x \right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 30
dsolve(y(x)^2+(x*sqrt(y(x)^2-x^2)-x*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ \frac {\sqrt {y \relax (x )^{2}-x^{2}}}{y \relax (x ) x}+\frac {1}{x}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 2.258 (sec). Leaf size: 111
DSolve[y[x]^2+(x*Sqrt[y[x]^2-x^2]-x*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\frac {\sqrt {\frac {y(x)^2}{x^2}-1} \left (\log \left (\sqrt {\frac {y(x)}{x}+1}-1\right )+\log \left (\sqrt {\frac {y(x)}{x}+1}+1\right )\right )}{\sqrt {\frac {y(x)}{x}-1} \sqrt {\frac {y(x)}{x}+1}}-2 \log \left (\sqrt {\frac {y(x)}{x}-1}-\sqrt {\frac {y(x)}{x}+1}\right )=\log (x)+c_1,y(x)\right ] \]