74.9.17 problem 28

Internal problem ID [16193]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.1, page 141
Problem number : 28
Date solved : Tuesday, January 28, 2025 at 08:56:55 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+10 y^{\prime }+25 y&=0 \end{align*}

Using reduction of order method given that one solution is

\begin{align*} y&={\mathrm e}^{-5 t} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 14

dsolve([diff(y(t),t$2)+10*diff(y(t),t)+25*y(t)=0,exp(-5*t)],singsol=all)
 

\[ y = {\mathrm e}^{-5 t} \left (c_{2} t +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 18

DSolve[D[y[t],{t,2}]+10*D[y[t],t]+25*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-5 t} (c_2 t+c_1) \]