64.8.9 problem 12

Internal problem ID [13397]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.1. Basic theory of linear differential equations. Exercises page 113
Problem number : 12
Date solved : Tuesday, January 28, 2025 at 05:41:45 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+5 y^{\prime }+12 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

dsolve(diff(y(x),x$3)-6*diff(y(x),x$2)+5*diff(y(x),x)+12*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{3 x} c_{1} +c_{2} {\mathrm e}^{-x}+c_{3} {\mathrm e}^{4 x} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 29

DSolve[D[y[x],{x,3}]-6*D[y[x],{x,2}]+5*D[y[x],x]+12*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (e^{4 x} \left (c_3 e^x+c_2\right )+c_1\right ) \]