87.2.9 problem 9

Internal problem ID [23244]
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 17
Problem number : 9
Date solved : Thursday, October 02, 2025 at 09:26:44 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (2\right )&=3 \\ \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 9

ode:=x*diff(y(x),x)-y(x) = 1; 
ic:=[y(2) = 3]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 2 x -1 \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 10

ode=x*D[y[x],x]-y[x]==1; 
ic={y[2]==3}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 2 x-1 \end{align*}

✓ Sympy. Time used: 0.134 (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 = {y(2): 3} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 2 x - 1 \]