28.1.121 problem 144

Internal problem ID [4427]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 144
Date solved : Monday, January 27, 2025 at 09:16:57 AM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 23

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

\[ x -y \left (x \right )^{2}+y \left (x \right )-{\mathrm e}^{-y \left (x \right )} c_{1} y \left (x \right ) = 0 \]

✓ Solution by Mathematica

Time used: 0.162 (sec). Leaf size: 24

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

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