44.1.42 problem 44

Internal problem ID [6917]
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 : Monday, January 27, 2025 at 02:34:57 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 30

dsolve(diff(y(x),x$2)+4*diff(y(x),x)+6*y(x)=10,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 41

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

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