60.1.294 problem 295

Internal problem ID [10308]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 295
Date solved : Monday, January 27, 2025 at 07:06:04 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} x \left (y^{2}+y x -x^{2}\right ) y^{\prime }-y^{3}+x y^{2}+x^{2} y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.258 (sec). Leaf size: 29

dsolve(x*(y(x)^2+x*y(x)-x^2)*diff(y(x),x)-y(x)^3+x*y(x)^2+x^2*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.211 (sec). Leaf size: 34

DSolve[x*(y[x]^2+x*y[x]-x^2)*D[y[x],x]-y[x]^3+x*y[x]^2+x^2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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