74.11.21 problem 33

Internal problem ID [16271]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.3, page 156
Problem number : 33
Date solved : Tuesday, January 28, 2025 at 08:59:45 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }&=52 \sin \left (3 t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 25

dsolve(diff(y(t),t$2)-2*diff(y(t),t)=52*sin(3*t),y(t), singsol=all)
 

\[ y = \frac {c_{1} {\mathrm e}^{2 t}}{2}-4 \sin \left (3 t \right )+\frac {8 \cos \left (3 t \right )}{3}+c_{2} \]

✓ Solution by Mathematica

Time used: 5.213 (sec). Leaf size: 46

DSolve[D[y[t],{t,2}]-2*D[y[t],t]==52*Sin[3*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \int _1^te^{2 K[2]} \left (c_1+\int _1^{K[2]}52 e^{-2 K[1]} \sin (3 K[1])dK[1]\right )dK[2]+c_2 \]