10.1.27 problem 27

Internal problem ID [1124]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.1. Page 40
Problem number : 27
Date solved : Monday, January 27, 2025 at 04:34:51 AM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

\begin{align*} y \left (0\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 19

dsolve([1/2*y(t)+diff(y(t),t) = 2*cos(t),y(0) = -1],y(t), singsol=all)
 

\[ y = \frac {4 \cos \left (t \right )}{5}+\frac {8 \sin \left (t \right )}{5}-\frac {9 \,{\mathrm e}^{-\frac {t}{2}}}{5} \]

✓ Solution by Mathematica

Time used: 0.046 (sec). Leaf size: 27

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

\[ y(t)\to \frac {1}{5} \left (-9 e^{-t/2}+8 \sin (t)+4 \cos (t)\right ) \]