72.8.12 problem 25

Internal problem ID [14776]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Review Exercises for chapter 1. page 136
Problem number : 25
Date solved : Tuesday, January 28, 2025 at 07:15:01 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }&=-5 y+\sin \left (3 t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 23

dsolve(diff(y(t),t)= -5*y(t)+sin(3*t),y(t), singsol=all)
 

\[ y = -\frac {3 \cos \left (3 t \right )}{34}+\frac {5 \sin \left (3 t \right )}{34}+{\mathrm e}^{-5 t} c_{1} \]

✓ Solution by Mathematica

Time used: 0.087 (sec). Leaf size: 33

DSolve[D[y[t],t]==-5*y[t]+Sin[3*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-5 t} \left (\int _1^te^{5 K[1]} \sin (3 K[1])dK[1]+c_1\right ) \]