Internal problem ID [2643]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x y^{3}+\left (1+y\right ) {\mathrm e}^{-x} y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 71
dsolve(x*y(x)^3+(y(x)+1)*exp(-x)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {-1+\sqrt {2 x \,{\mathrm e}^{x}-2 \,{\mathrm e}^{x}+2 c_{1}+1}}{2 \left (x \,{\mathrm e}^{x}-{\mathrm e}^{x}+c_{1}\right )} \\ y \relax (x ) = \frac {1+\sqrt {2 x \,{\mathrm e}^{x}-2 \,{\mathrm e}^{x}+2 c_{1}+1}}{2 x \,{\mathrm e}^{x}-2 \,{\mathrm e}^{x}+2 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 9.967 (sec). Leaf size: 60
DSolve[x*y[x]^3+(y[x]+1)*Exp[-x]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{1+\sqrt {2 e^x (x-1)+1-2 c_1}} \\ y(x)\to \frac {1}{-1+\sqrt {2 e^x (x-1)+1-2 c_1}} \\ y(x)\to 0 \\ \end{align*}