74.11.41 problem 53

Internal problem ID [16291]
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 : 53
Date solved : Tuesday, January 28, 2025 at 09:00:41 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+6 y^{\prime }+25 y&=-1 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-{\frac {1}{25}}\\ y^{\prime }\left (0\right )&=7 \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 16

dsolve([diff(y(t),t$2)+6*diff(y(t),t)+25*y(t)=-1,y(0) = -1/25, D(y)(0) = 7],y(t), singsol=all)
 

\[ y = \frac {7 \,{\mathrm e}^{-3 t} \sin \left (4 t \right )}{4}-\frac {1}{25} \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 22

DSolve[{D[y[t],{t,2}]+6*D[y[t],t]+25*y[t]==-1,{y[0]==-1/25,Derivative[1][y][0] ==7}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {7}{4} e^{-3 t} \sin (4 t)-\frac {1}{25} \]