10.1.11 problem 11

Internal problem ID [1108]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.1. Page 40
Problem number : 11
Date solved : Monday, January 27, 2025 at 04:33:42 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y+y^{\prime }&=5 \sin \left (2 t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 21

dsolve(y(t)+diff(y(t),t) = 5*sin(2*t),y(t), singsol=all)
 

\[ y = -2 \cos \left (2 t \right )+\sin \left (2 t \right )+{\mathrm e}^{-t} c_1 \]

✓ Solution by Mathematica

Time used: 0.080 (sec). Leaf size: 24

DSolve[y[t]+D[y[t],t] == 5*Sin[2*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \sin (2 t)-2 \cos (2 t)+c_1 e^{-t} \]