40.3.9 problem 23 (o)

Internal problem ID [6613]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 5. Equations of first order and first degree (Exact equations). Supplemetary problems. Page 33
Problem number : 23 (o)
Date solved : Monday, January 27, 2025 at 02:15:54 PM
CAS classification : [_exact, _rational]

\begin{align*} y^{2}-\frac {y}{x \left (x +y\right )}+2+\left (\frac {1}{x +y}+2 y \left (1+x \right )\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 129

dsolve((y(x)^2- y(x)/(x*(x+y(x)))+2)+( 1/(x+y(x)) + 2*y(x)*(1+x))*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = -x \left ({\mathrm e}^{\operatorname {RootOf}\left (x^{3} {\mathrm e}^{2 \textit {\_Z}}+x^{2} {\mathrm e}^{2 \textit {\_Z}}-2 x^{3} {\mathrm e}^{\textit {\_Z}}+c_1 \,{\mathrm e}^{2 \textit {\_Z}}-\textit {\_Z} \,{\mathrm e}^{2 \textit {\_Z}}+2 x \,{\mathrm e}^{2 \textit {\_Z}}-2 x^{2} {\mathrm e}^{\textit {\_Z}}+x^{3}+x^{2}\right )}-1\right ) {\mathrm e}^{-\operatorname {RootOf}\left (x^{3} {\mathrm e}^{2 \textit {\_Z}}+x^{2} {\mathrm e}^{2 \textit {\_Z}}-2 x^{3} {\mathrm e}^{\textit {\_Z}}+c_1 \,{\mathrm e}^{2 \textit {\_Z}}-\textit {\_Z} \,{\mathrm e}^{2 \textit {\_Z}}+2 x \,{\mathrm e}^{2 \textit {\_Z}}-2 x^{2} {\mathrm e}^{\textit {\_Z}}+x^{3}+x^{2}\right )} \]

✓ Solution by Mathematica

Time used: 0.519 (sec). Leaf size: 29

DSolve[(y[x]^2- y[x]/(x*(x+y[x]))+2)+( 1/(x+y[x]) + 2*y[x]*(1+x))*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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