74.5.52 problem 59

Internal problem ID [16016]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.3, page 49
Problem number : 59
Date solved : Tuesday, January 28, 2025 at 08:26:35 AM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 17

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

\[ y = \cos \left (t \right )+\sin \left (t \right )+t -1+{\mathrm e}^{-t} c_{1} \]

✓ Solution by Mathematica

Time used: 0.072 (sec). Leaf size: 34

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

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