Internal problem ID [2708]
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: 75.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {\left (x +1\right ) \left (y^{\prime }+y^{2}\right )-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 21
dsolve((1+x)*(diff(y(x),x)+y(x)^2)-y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {2 x +2}{x^{2}+2 c_{1}+2 x} \]
✓ Solution by Mathematica
Time used: 0.177 (sec). Leaf size: 27
DSolve[(1+x)*(y'[x]+y[x]^2)-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2 (x+1)}{x (x+2)+2 c_1} \\ y(x)\to 0 \\ \end{align*}