7.10.36 problem 36

Internal problem ID [306]
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 : 36
Date solved : Wednesday, February 05, 2025 at 03:18:19 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 9 y^{\prime \prime \prime }+11 y^{\prime \prime }+4 y^{\prime }-14 y&=0 \end{align*}

Using reduction of order method given that one solution is

\begin{align*} y&={\mathrm e}^{-x} \sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 24

dsolve([9*diff(y(x),x$3)+11*diff(y(x),x$2)+4*diff(y(x),x)-14*y(x)=0,exp(-x)*sin(x)],singsol=all)
 

\[ y = \left (c_1 \,{\mathrm e}^{\frac {16 x}{9}}+c_2 \sin \left (x \right )+\cos \left (x \right ) c_3 \right ) {\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 32

DSolve[9*D[y[x],{x,3}]+11*D[y[x],{x,2}]+4*D[y[x],x]-14*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (c_3 e^{16 x/9}+c_2 \cos (x)+c_1 \sin (x)\right ) \]