38.6.14 problem 14

Internal problem ID [8444]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.3 Linear equations. Exercises 2.3 at page 63
Problem number : 14
Date solved : Tuesday, September 30, 2025 at 05:36:56 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 20

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

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

✓ Mathematica. Time used: 0.064 (sec). Leaf size: 33

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

\begin{align*} y(x)&\to \frac {e^{-x-1} \left (\int _1^xe \sin (2 K[1])dK[1]+c_1\right )}{x} \end{align*}

✓ Sympy. Time used: 3.188 (sec). Leaf size: 15

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

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