88.6.10 problem 10

Internal problem ID [23992]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Exercise at page 38
Problem number : 10
Date solved : Thursday, October 02, 2025 at 09:49:56 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=1+\frac {3 y}{x} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

ode:=diff(y(x),x) = 1+3*y(x)/x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {1}{2} x +c_1 \,x^{3} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 17

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

\begin{align*} y(x)&\to -\frac {x}{2}+c_1 x^3 \end{align*}

✓ Sympy. Time used: 0.141 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - 1 - 3*y(x)/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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