64.10.16 problem 16

Internal problem ID [13422]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.2. The homogeneous linear equation with constant coefficients. Exercises page 135
Problem number : 16
Date solved : Tuesday, January 28, 2025 at 05:42:14 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }+5 y^{\prime }+6 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 37

dsolve(diff(y(x),x$3)+4*diff(y(x),x$2)+5*diff(y(x),x)+6*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} {\mathrm e}^{-3 x}+c_{2} {\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {7}\, x}{2}\right )+c_{3} {\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {7}\, x}{2}\right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 56

DSolve[D[y[x],{x,3}]+4*D[y[x],{x,2}]+5*D[y[x],x]+6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-3 x} \left (c_2 e^{5 x/2} \cos \left (\frac {\sqrt {7} x}{2}\right )+c_1 e^{5 x/2} \sin \left (\frac {\sqrt {7} x}{2}\right )+c_3\right ) \]