7.10.33 problem 33

Internal problem ID [303]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.3 (Homogeneous equations with constant coefficients). Problems at page 134
Problem number : 33
Date solved : Wednesday, February 05, 2025 at 03:18:18 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-54 y&=0 \end{align*}

Using reduction of order method given that one solution is

\begin{align*} y&={\mathrm e}^{3 x} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 31

dsolve([diff(y(x),x$3)+3*diff(y(x),x$2)-54*y(x)=0,exp(3*x)],singsol=all)
 

\[ y = c_1 \,{\mathrm e}^{3 x}+c_2 \,{\mathrm e}^{-3 x} \sin \left (3 x \right )+c_3 \,{\mathrm e}^{-3 x} \cos \left (3 x \right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 34

DSolve[D[y[x],{x,3}]+3*D[y[x],{x,2}]-54*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-3 x} \left (c_3 e^{6 x}+c_2 \cos (3 x)+c_1 \sin (3 x)\right ) \]