74.18.20 problem 26

Internal problem ID [16577]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number : 26
Date solved : Tuesday, January 28, 2025 at 09:11:12 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }&=-3 \sin \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 21

dsolve(diff(y(t),t$2)-4*diff(y(t),t)=-3*sin(t),y(t), singsol=all)
 

\[ y = \frac {{\mathrm e}^{4 t} c_{1}}{4}+\frac {3 \sin \left (t \right )}{17}-\frac {12 \cos \left (t \right )}{17}+c_{2} \]

✓ Solution by Mathematica

Time used: 5.216 (sec). Leaf size: 44

DSolve[D[y[t],{t,2}]-4*D[y[t],t]==-3*Sin[t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \int _1^te^{4 K[2]} \left (c_1+\int _1^{K[2]}-3 e^{-4 K[1]} \sin (K[1])dK[1]\right )dK[2]+c_2 \]