81.6.10 problem 7-10

Internal problem ID [21556]
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 : 7-10
Date solved : Thursday, October 02, 2025 at 07:48:05 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }+\frac {\left (2 x +1\right ) y}{x}&={\mathrm e}^{-2 x} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

ode:=diff(y(x),x)+(2*x+1)/x*y(x) = exp(-2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (\frac {x^{2}}{2}+c_1 \right ) {\mathrm e}^{-2 x}}{x} \]

✓ Mathematica. Time used: 0.048 (sec). Leaf size: 25

ode=D[y[x],x]+ (2*x+1)/x*y[x] ==Exp[-2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.197 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - exp(-2*x) + (2*x + 1)*y(x)/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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