86.3.9 problem 7

Internal problem ID [23100]
Book : An introduction to Differential Equations. By Howard Frederick Cleaves. 1969. Oliver and Boyd publisher. ISBN 0050015044
Section : Chapter 4. Linear equations of the first order. Exercise 4a at page 56
Problem number : 7
Date solved : Thursday, October 02, 2025 at 09:21:49 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }-\frac {3 y}{x}&=5 x \end{align*}

With initial conditions

\begin{align*} y \left ({\mathrm e}\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.016 (sec). Leaf size: 15

ode:=diff(y(x),x)-3*y(x)/x = 5*x; 
ic:=[y(exp(1)) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 5 \left ({\mathrm e}^{-1} x -1\right ) x^{2} \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 18

ode=D[y[x],x]-3*y[x]/x==5*x; 
ic={y[Exp[1]]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {5 x^2 (x-e)}{e} \end{align*}

✓ Sympy. Time used: 0.156 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-5*x + Derivative(y(x), x) - 3*y(x)/x,0) 
ics = {y(E): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x^{2} \left (\frac {5 x}{e} - 5\right ) \]