38.1.42 problem 44

Internal problem ID [8203]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Exercises 1.1 at page 12
Problem number : 44
Date solved : Tuesday, September 30, 2025 at 05:18:45 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }+6 y&=10 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 30

ode:=diff(diff(y(x),x),x)+4*diff(y(x),x)+6*y(x) = 10; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-2 x} \sin \left (\sqrt {2}\, x \right ) c_2 +{\mathrm e}^{-2 x} \cos \left (\sqrt {2}\, x \right ) c_1 +\frac {5}{3} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 41

ode=D[y[x],{x,2}]+4*D[y[x],x]+6*y[x]==10; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_2 e^{-2 x} \cos \left (\sqrt {2} x\right )+c_1 e^{-2 x} \sin \left (\sqrt {2} x\right )+\frac {5}{3} \end{align*}

✓ Sympy. Time used: 0.118 (sec). Leaf size: 31

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(6*y(x) + 4*Derivative(y(x), x) + Derivative(y(x), (x, 2)) - 10,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} \sin {\left (\sqrt {2} x \right )} + C_{2} \cos {\left (\sqrt {2} x \right )}\right ) e^{- 2 x} + \frac {5}{3} \]