74.18.17 problem 23

Internal problem ID [16574]
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 : 23
Date solved : Tuesday, January 28, 2025 at 09:11:08 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 9 y^{\prime \prime \prime }+12 y^{\prime \prime }+13 y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 22

dsolve(9*diff(y(x),x$3)+12*diff(y(x),x$2)+13*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 60.042 (sec). Leaf size: 37

DSolve[9*D[y[x],{x,3}]+12*D[y[x],{x,2}]+13*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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