10.1.23 problem 23

Internal problem ID [1120]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.1. Page 40
Problem number : 23
Date solved : Monday, January 27, 2025 at 04:34:06 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} -2 y+3 y^{\prime }&={\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: 0.018 (sec). Leaf size: 35

dsolve([-2*y(t)+3*diff(y(t),t) = exp(-1/2*Pi*t),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: 0.088 (sec). Leaf size: 43

DSolve[{-2*y[t]+3*D[y[t],t] == Exp[-1/2*Pi*t],y[0]==a},y[t],t,IncludeSingularSolutions -> True]
 

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