29.25.1 problem 698

Internal problem ID [5288]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 25
Problem number : 698
Date solved : Monday, January 27, 2025 at 11:04:31 AM
CAS classification : [_rational]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 29

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

\[ y \left (x \right ) = {\mathrm e}^{\operatorname {RootOf}\left (-{\mathrm e}^{3 \textit {\_Z}}-{\mathrm e}^{\textit {\_Z}} \ln \left (x \right )+c_{1} {\mathrm e}^{\textit {\_Z}}-\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+x \right )} \]

✓ Solution by Mathematica

Time used: 0.233 (sec). Leaf size: 23

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

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