74.5.40 problem 47

Internal problem ID [16004]
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 : 47
Date solved : Tuesday, January 28, 2025 at 08:26:15 AM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 21

dsolve(diff(y(t),t)-y(t)=sin(2*t),y(t), singsol=all)
 

\[ y = -\frac {2 \cos \left (2 t \right )}{5}-\frac {\sin \left (2 t \right )}{5}+c_{1} {\mathrm e}^{t} \]

✓ Solution by Mathematica

Time used: 0.043 (sec). Leaf size: 31

DSolve[D[y[t],t]-y[t]==Sin[2*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^t \left (\int _1^te^{-K[1]} \sin (2 K[1])dK[1]+c_1\right ) \]