29.23.16 problem 647

Internal problem ID [5238]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 23
Problem number : 647
Date solved : Monday, January 27, 2025 at 10:38:32 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.296 (sec). Leaf size: 29

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

\[ y \left (x \right ) = {\mathrm e}^{\operatorname {RootOf}\left (2 \,{\mathrm e}^{\textit {\_Z}} \ln \left (x \right )+{\mathrm e}^{2 \textit {\_Z}}+2 c_{1} {\mathrm e}^{\textit {\_Z}}+\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+1\right )} x \]

✓ Solution by Mathematica

Time used: 0.191 (sec). Leaf size: 34

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

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