7.10.34 problem 34

Internal problem ID [304]
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 : 34
Date solved : Wednesday, February 05, 2025 at 03:18:18 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 3 y^{\prime \prime \prime }-2 y^{\prime \prime }+12 y^{\prime }-8 y&=0 \end{align*}

Using reduction of order method given that one solution is

\begin{align*} y&={\mathrm e}^{\frac {2 x}{3}} \end{align*}

✓ Solution by Maple

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

dsolve([3*diff(y(x),x$3)-2*diff(y(x),x$2)+12*diff(y(x),x)-8*y(x)=0,exp(2*x/3)],singsol=all)
 

\[ y = c_1 \,{\mathrm e}^{\frac {2 x}{3}}+\sin \left (2 x \right ) c_2 +\cos \left (2 x \right ) c_3 \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 30

DSolve[3*D[y[x],{x,3}]-2*D[y[x],{x,2}]+12*D[y[x],x]-8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_3 e^{2 x/3}+c_1 \cos (2 x)+c_2 \sin (2 x) \]