39.1.5 problem Problem 11.5

Internal problem ID [6510]
Book : Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill 2014
Section : Chapter 11. THE METHOD OF UNDETERMINED COEFFICIENTS. page 95
Problem number : Problem 11.5
Date solved : Monday, January 27, 2025 at 02:10:36 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+25 y&=64 \,{\mathrm e}^{-t} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 31

dsolve(diff(y(t),t$2)-6*diff(y(t),t)+25*y(t)=64*exp(-t),y(t), singsol=all)
 

\[ y = {\mathrm e}^{3 t} \sin \left (4 t \right ) c_2 +{\mathrm e}^{3 t} \cos \left (4 t \right ) c_1 +2 \,{\mathrm e}^{-t} \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 37

DSolve[D[y[t],{t,2}]-6*D[y[t],t]+25*y[t]==64*Exp[-t],y[t],t,IncludeSingularSolutions -> True]
 

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