Internal problem ID [3152]
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]
\[ \boxed {x y^{3}+\left (y+1\right ) {\mathrm e}^{-x} y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (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 {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}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 9.963 (sec). Leaf size: 88
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-\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*}