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 : Sunday, March 30, 2025 at 03:17:39 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

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

\[ y = \frac {{\mathrm e}^{x} c_1 -1}{x} \]

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

ode=(y[x]-1-x*y[x])+(x)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.253 (sec). Leaf size: 10

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

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