10.1.29 problem 29

Internal problem ID [1126]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.1. Page 40
Problem number : 29
Date solved : Monday, January 27, 2025 at 04:34:55 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} \frac {y}{4}+y^{\prime }&=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: 0.008 (sec). Leaf size: 24

dsolve([1/4*y(t)+diff(y(t),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: 0.140 (sec). Leaf size: 32

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

\[ y(t)\to \frac {4}{65} \left (-197 e^{-t/4}+16 \sin (2 t)+2 \cos (2 t)+195\right ) \]