74.5.54 problem 60 (b)

Internal problem ID [16018]
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 : 60 (b)
Date solved : Tuesday, January 28, 2025 at 08:26:39 AM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 25

dsolve([diff(y(t),t)-y(t)/2=sin(t),y(0) = a],y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.058 (sec). Leaf size: 34

DSolve[{D[y[t],t]-y[t]/2==Sin[t],{y[0]==a}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{t/2} \left (\int _0^te^{-\frac {K[1]}{2}} \sin (K[1])dK[1]+a\right ) \]