76.2.21 problem 21

Internal problem ID [17357]
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 : 21
Date solved : Tuesday, January 28, 2025 at 10:02:17 AM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 25

dsolve([diff(y(t),t)-1/3*y(t)=3*cos(t),y(0) = a],y(t), singsol=all)
 

\[ y = -\frac {9 \cos \left (t \right )}{10}+\frac {27 \sin \left (t \right )}{10}+{\mathrm e}^{\frac {t}{3}} a +\frac {9 \,{\mathrm e}^{\frac {t}{3}}}{10} \]

✓ Solution by Mathematica

Time used: 0.061 (sec). Leaf size: 35

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

\[ y(t)\to e^{t/3} \left (\int _0^t3 e^{-\frac {K[1]}{3}} \cos (K[1])dK[1]+a\right ) \]