72.8.18 problem 31

Internal problem ID [14782]
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 : 31
Date solved : Tuesday, January 28, 2025 at 07:15:13 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }&=2 y+\cos \left (4 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)= 2*y(t)+cos(4*t),y(0) = 1],y(t), singsol=all)
 

\[ y = -\frac {\cos \left (4 t \right )}{10}+\frac {\sin \left (4 t \right )}{5}+\frac {11 \,{\mathrm e}^{2 t}}{10} \]

✓ Solution by Mathematica

Time used: 0.088 (sec). Leaf size: 32

DSolve[{D[y[t],t]==2*y[t]+Cos[4*t],{y[0]==1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{2 t} \left (\int _0^te^{-2 K[1]} \cos (4 K[1])dK[1]+1\right ) \]