32.6.48 problem Exercise 12.48, page 103

Internal problem ID [5913]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous Methods
Problem number : Exercise 12.48, page 103
Date solved : Monday, January 27, 2025 at 01:27:18 PM
CAS classification : [_rational]

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 29

dsolve((2*x*y(x)^3+x*y(x)+x^2)*diff(y(x),x)-x*y(x)+y(x)^2=0,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: 0.255 (sec). Leaf size: 23

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

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