74.10.37 problem 39

Internal problem ID [16242]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.2, page 147
Problem number : 39
Date solved : Tuesday, January 28, 2025 at 08:58:26 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} a y^{\prime \prime }+2 b y^{\prime }+c y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 48

dsolve(a*diff(y(t),t$2)+2*b*diff(y(t),t)+c*y(t)=0,y(t), singsol=all)
 

\[ y = c_{1} {\mathrm e}^{\frac {\left (-b +\sqrt {-a c +b^{2}}\right ) t}{a}}+c_{2} {\mathrm e}^{-\frac {\left (b +\sqrt {-a c +b^{2}}\right ) t}{a}} \]

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 54

DSolve[a*D[y[t],{t,2}]+2*b*D[y[t],t]+c*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-\frac {t \left (\sqrt {b^2-a c}+b\right )}{a}} \left (c_2 e^{\frac {2 t \sqrt {b^2-a c}}{a}}+c_1\right ) \]