Internal problem ID [4980]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 1. First order differential equations. Section 1.1 Separable equations problems. page
7
Problem number: 20.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\left (y-1\right ) \left (1+x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve(diff(y(x),x)=(y(x)-1)*(x+1),y(x), singsol=all)
\[ y \relax (x ) = 1+{\mathrm e}^{\frac {x \left (x +2\right )}{2}} c_{1} \]
✓ Solution by Mathematica
Time used: 0.132 (sec). Leaf size: 25
DSolve[y'[x]==(y[x]-1)*(x+1),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 1+c_1 e^{\frac {1}{2} x (x+2)} \\ y(x)\to 1 \\ \end{align*}