74.18.14 problem 20

Internal problem ID [16571]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number : 20
Date solved : Tuesday, January 28, 2025 at 09:11:06 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 12 y^{\prime \prime }+8 y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

dsolve(12*diff(y(x),x$2)+8*diff(y(x),x)+y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} {\mathrm e}^{-\frac {x}{6}}+{\mathrm e}^{-\frac {x}{2}} c_{2} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 26

DSolve[12*D[y[x],{x,2}]+8*D[y[x],x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x/2} \left (c_1 e^{x/3}+c_2\right ) \]