64.5.10 problem 10

Internal problem ID [13323]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.3 (Linear equations). Exercises page 56
Problem number : 10
Date solved : Tuesday, January 28, 2025 at 05:22:11 AM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

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

✓ Solution by Maple

Time used: 0.092 (sec). Leaf size: 35

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

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

✓ Solution by Mathematica

Time used: 0.199 (sec). Leaf size: 29

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

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