87.3.9 problem 9

Internal problem ID [23258]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 1. Elementary methods. First order differential equations. Exercise at page 26
Problem number : 9
Date solved : Thursday, October 02, 2025 at 09:27:16 PM
CAS classification : [_separable]

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

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

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

\[ y = 1+{\mathrm e}^{-\frac {x \left (x +2\right )}{2}} c_1 \]

✓ Mathematica. Time used: 0.068 (sec). Leaf size: 25

ode=D[y[x],x]==x-x*y[x]-y[x]+1; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.165 (sec). Leaf size: 15

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

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