47.1.20 problem 20

Internal problem ID [7401]
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
Date solved : Monday, January 27, 2025 at 02:52:47 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 15

dsolve(diff(y(x),x)=(y(x)-1)*(x+1),y(x), singsol=all)
 

\[ y = 1+c_{1} {\mathrm e}^{\frac {x \left (x +2\right )}{2}} \]

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 25

DSolve[D[y[x],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*}