74.8.9 problem 9

Internal problem ID [16145]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Review exercises, page 80
Problem number : 9
Date solved : Tuesday, January 28, 2025 at 08:51:58 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+3 y&=-10 \sin \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 17

dsolve(diff(y(t),t)+3*y(t)=-10*sin(t),y(t), singsol=all)
 

\[ y = \cos \left (t \right )-3 \sin \left (t \right )+{\mathrm e}^{-3 t} c_{1} \]

✓ Solution by Mathematica

Time used: 0.054 (sec). Leaf size: 32

DSolve[D[y[t],t]+3*y[t]==-10*Sin[t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-3 t} \left (\int _1^t-10 e^{3 K[1]} \sin (K[1])dK[1]+c_1\right ) \]