81.6.13 problem 7-13

Internal problem ID [21559]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 7. Linear Differential Equations. Page 101.
Problem number : 7-13
Date solved : Thursday, October 02, 2025 at 07:48:11 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 9

ode:=diff(y(x),x)-y(x)/x = x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (x +c_1 \right ) x \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 11

ode=D[y[x],x]-y[x]/x ==x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.121 (sec). Leaf size: 7

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

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