73.12.10 problem 19.2 (d)

Internal problem ID [15362]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 19. Arbitrary Homogeneous linear equations with constant coefficients. Additional exercises page 369
Problem number : 19.2 (d)
Date solved : Tuesday, January 28, 2025 at 07:53:47 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-9 y^{\prime \prime }+31 y^{\prime }-39 y&=0 \end{align*}

✓ Solution by Maple

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

dsolve(diff(y(x),x$3)-9*diff(y(x),x$2)+31*diff(y(x),x)-39*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 28

DSolve[D[y[x],{x,3}]-9*D[y[x],{x,2}]+31*D[y[x],x]-39*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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