72.6.3 problem 3

Internal problem ID [14728]
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. Exercises section 1.8 page 121
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 07:12:57 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }&=-3 y+4 \cos \left (2 t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 23

dsolve(diff(y(t),t)=-3*y(t)+4*cos(2*t),y(t), singsol=all)
 

\[ y = \frac {12 \cos \left (2 t \right )}{13}+\frac {8 \sin \left (2 t \right )}{13}+{\mathrm e}^{-3 t} c_{1} \]

✓ Solution by Mathematica

Time used: 0.090 (sec). Leaf size: 34

DSolve[D[y[t],t]==-3*y[t]+4*Cos[2*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-3 t} \left (\int _1^t4 e^{3 K[1]} \cos (2 K[1])dK[1]+c_1\right ) \]