76.2.29 problem 29

Internal problem ID [17365]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.2 (Linear equations: Method of integrating factors). Problems at page 54
Problem number : 29
Date solved : Tuesday, January 28, 2025 at 10:03:09 AM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 24

dsolve([diff(y(t),t)+1/4*y(t)=3+2*cos(2*t),y(0) = 0],y(t), singsol=all)
 

\[ y = 12+\frac {8 \cos \left (2 t \right )}{65}+\frac {64 \sin \left (2 t \right )}{65}-\frac {788 \,{\mathrm e}^{-\frac {t}{4}}}{65} \]

✓ Solution by Mathematica

Time used: 0.163 (sec). Leaf size: 38

DSolve[{D[y[t],t]+1/4*y[t]==3+2*Cos[2*t],{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-t/4} \int _0^te^{\frac {K[1]}{4}} (2 \cos (2 K[1])+3)dK[1] \]