74.11.22 problem 34

Internal problem ID [16272]
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 : 34
Date solved : Tuesday, January 28, 2025 at 08:59:48 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=25 \sin \left (2 t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 36

dsolve(diff(y(t),t$2)-6*diff(y(t),t)+13*y(t)=25*sin(2*t),y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 38

DSolve[D[y[t],{t,2}]-6*D[y[t],t]+13*y[t]==25*Sin[2*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \left (\frac {4}{3}+c_2 e^{3 t}\right ) \cos (2 t)+\left (1+c_1 e^{3 t}\right ) \sin (2 t) \]