74.9.24 problem 35

Internal problem ID [16200]
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 : 35
Date solved : Tuesday, January 28, 2025 at 08:57:00 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 49

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

\[ y = c_{1} {\mathrm e}^{\frac {\left (-b +\sqrt {-4 a c +b^{2}}\right ) t}{2 a}}+c_{2} {\mathrm e}^{-\frac {\left (b +\sqrt {-4 a c +b^{2}}\right ) t}{2 a}} \]

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 55

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

\[ y(t)\to e^{-\frac {t \left (\sqrt {b^2-4 a c}+b\right )}{2 a}} \left (c_2 e^{\frac {t \sqrt {b^2-4 a c}}{a}}+c_1\right ) \]