32.1.2 problem First order with homogeneous Coefficients. Exercise 7.3, page 61

Internal problem ID [5772]
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
Date solved : Monday, January 27, 2025 at 01:16:18 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} \left (x +\sqrt {y^{2}-y x}\right ) y^{\prime }-y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 33

dsolve((x+sqrt(y(x)^2-x*y(x)))*diff(y(x),x)-y(x)=0,y(x), singsol=all)
 

\[ \frac {\ln \left (y \left (x \right )\right ) y \left (x \right )-c_{1} y \left (x \right )+2 \sqrt {y \left (x \right ) \left (-x +y \left (x \right )\right )}}{y \left (x \right )} = 0 \]

✓ Solution by Mathematica

Time used: 1.756 (sec). Leaf size: 69

DSolve[(x+Sqrt[y[x]^2-x*y[x]])*D[y[x],x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\frac {\frac {2 y(x)}{x}+\sqrt {\frac {y(x) \left (\frac {y(x)}{x}-1\right )}{x}} \log \left (\frac {y(x)}{x}\right )-2}{\sqrt {\frac {y(x)}{x}} \sqrt {\frac {y(x)}{x}-1}}=-\log (x)+c_1,y(x)\right ] \]