44.1.50 problem 56

Internal problem ID [6925]
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 : 56
Date solved : Monday, January 27, 2025 at 02:35:54 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+4 y&=5 \sin \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 37

dsolve(diff(y(t),t$2)+2*diff(y(t),t)+4*y(t)=5*sin(t),y(t), singsol=all)
 

\[ y = {\mathrm e}^{-t} \sin \left (\sqrt {3}\, t \right ) c_{2} +{\mathrm e}^{-t} \cos \left (\sqrt {3}\, t \right ) c_{1} +\frac {15 \sin \left (t \right )}{13}-\frac {10 \cos \left (t \right )}{13} \]

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 51

DSolve[D[y[t],{t,2}]+2*D[y[t],t]+4*y[t]==5*Sin[t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -\frac {5}{13} (2 \cos (t)-3 \sin (t))+c_2 e^{-t} \cos \left (\sqrt {3} t\right )+c_1 e^{-t} \sin \left (\sqrt {3} t\right ) \]