44.5.25 problem 25

Internal problem ID [7087]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 25
Date solved : Tuesday, January 28, 2025 at 08:48:17 PM
CAS classification : [_separable]

\begin{align*} x^{2} y^{\prime }&=y-y x \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 18

dsolve([x^2*diff(y(x),x)=y(x)-x*y(x),y(-1) = -1],y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{\frac {-x -1}{x}}}{x} \]

✓ Solution by Mathematica

Time used: 0.049 (sec). Leaf size: 18

DSolve[{x^2*D[y[x],x]==y[x]-x*y[x],{y[-1]==-1}},y[x],x,IncludeSingularSolutions -> True]
 

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