28.1.98 problem 121

Internal problem ID [4404]
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 : 121
Date solved : Monday, January 27, 2025 at 09:14:52 AM
CAS classification : [_linear]

\begin{align*} y-1-y x +x y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 14

dsolve((y(x)-1-x*y(x))+(x)*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 17

DSolve[(y[x]-1-x*y[x])+(x)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {-1+c_1 e^x}{x} \]