76.2.23 problem 23

Internal problem ID [17359]
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 : 23
Date solved : Tuesday, January 28, 2025 at 10:02:20 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} 3 y^{\prime }-2 y&={\mathrm e}^{-\frac {\pi t}{2}} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.037 (sec). Leaf size: 35

dsolve([3*diff(y(t),t)-2*y(t)=exp(-Pi*t/2),y(0) = a],y(t), singsol=all)
 

\[ y = \frac {\left (3 \pi a -2 \,{\mathrm e}^{t \left (-\frac {\pi }{2}-\frac {2}{3}\right )}+4 a +2\right ) {\mathrm e}^{\frac {2 t}{3}}}{3 \pi +4} \]

✓ Solution by Mathematica

Time used: 0.092 (sec). Leaf size: 43

DSolve[{3*D[y[t],t]-2*y[t]==Exp[-Pi*t/2],{y[0]==a}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {e^{2 t/3} \left ((4+3 \pi ) a-2 e^{-\frac {1}{6} (4+3 \pi ) t}+2\right )}{4+3 \pi } \]