74.18.16 problem 22

Internal problem ID [16573]
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 : 22
Date solved : Tuesday, January 28, 2025 at 09:11:07 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 9 y^{\prime \prime \prime }+36 y^{\prime \prime }+40 y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 26

dsolve(9*diff(y(x),x$3)+36*diff(y(x),x$2)+40*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = c_{1} +c_{2} {\mathrm e}^{-2 x} \sin \left (\frac {2 x}{3}\right )+c_{3} {\mathrm e}^{-2 x} \cos \left (\frac {2 x}{3}\right ) \]

✓ Solution by Mathematica

Time used: 60.106 (sec). Leaf size: 43

DSolve[9*D[y[x],{x,3}]+36*D[y[x],{x,2}]+40*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \int _1^xe^{-2 K[1]} \left (c_2 \cos \left (\frac {2 K[1]}{3}\right )+c_1 \sin \left (\frac {2 K[1]}{3}\right )\right )dK[1]+c_3 \]