72.6.10 problem 10

Internal problem ID [14735]
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 : 10
Date solved : Tuesday, January 28, 2025 at 07:13:09 AM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

\begin{align*} y \left (0\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 23

dsolve([diff(y(t),t)+3*y(t)=cos(2*t),y(0) = -1],y(t), singsol=all)
 

\[ y = \frac {3 \cos \left (2 t \right )}{13}+\frac {2 \sin \left (2 t \right )}{13}-\frac {16 \,{\mathrm e}^{-3 t}}{13} \]

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 32

DSolve[{D[y[t],t]+3*y[t]==Cos[2*t],{y[0]==-1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-3 t} \left (\int _0^te^{3 K[1]} \cos (2 K[1])dK[1]-1\right ) \]