84.14.1 problem 7.9

Internal problem ID [22158]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 7. Integrating factors. Supplementary problems
Problem number : 7.9
Date solved : Thursday, October 02, 2025 at 08:32:58 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.000 (sec). Leaf size: 9

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

\[ y = c_1 x -1 \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 16

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

\begin{align*} y(x)&\to -1+c_1 x\\ y(x)&\to -1 \end{align*}

✓ Sympy. Time used: 0.130 (sec). Leaf size: 7

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

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