74.18.15 problem 21

Internal problem ID [16572]
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 : 21
Date solved : Tuesday, January 28, 2025 at 09:11:07 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 2 y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 18

dsolve(2*diff(y(x),x$3)+3*diff(y(x),x$2)+diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = c_{1} +c_{2} {\mathrm e}^{-x}+c_{3} {\mathrm e}^{-\frac {x}{2}} \]

✓ Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 28

DSolve[2*D[y[x],{x,3}]+3*D[y[x],{x,2}]+D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -2 c_1 e^{-x/2}-c_2 e^{-x}+c_3 \]