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 : Sunday, March 30, 2025 at 11:40:10 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Maple. Time used: 0.030 (sec). Leaf size: 18

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

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

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

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

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

✓ Sympy. Time used: 0.382 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), x) + x*y(x) - y(x),0) 
ics = {y(-1): -1} 
dsolve(ode,func=y(x),ics=ics)
 

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