76.2.11 problem 11

Internal problem ID [17347]
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 : 11
Date solved : Tuesday, January 28, 2025 at 10:01:58 AM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

dsolve(diff(y(t),t)+y(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: 0.058 (sec). Leaf size: 32

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

\[ y(t)\to e^{-t} \left (\int _1^t5 e^{K[1]} \sin (2 K[1])dK[1]+c_1\right ) \]