28.1.7 problem 7

Internal problem ID [4313]
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 : 7
Date solved : Monday, January 27, 2025 at 09:01:49 AM
CAS classification : [_separable]

\begin{align*} x y^{3}+\left (y+1\right ) {\mathrm e}^{-x} y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 73

dsolve(x*y(x)^3+(y(x)+1)*exp(-x)*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \frac {1-\sqrt {\left (2 x -2\right ) {\mathrm e}^{x}+2 c_{1} +1}}{\left (2 x -2\right ) {\mathrm e}^{x}+2 c_{1}} \\ y \left (x \right ) &= \frac {\sqrt {\left (2 x -2\right ) {\mathrm e}^{x}+2 c_{1} +1}+1}{\left (2 x -2\right ) {\mathrm e}^{x}+2 c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 9.928 (sec). Leaf size: 88

DSolve[x*y[x]^3+(y[x]+1)*Exp[-x]*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1-\sqrt {2 e^x (x-1)+1-2 c_1}}{2 e^x (x-1)-2 c_1} \\ y(x)\to \frac {1+\sqrt {2 e^x (x-1)+1-2 c_1}}{2 e^x (x-1)-2 c_1} \\ y(x)\to 0 \\ \end{align*}