73.12.12 problem 19.2 (f)

Internal problem ID [15364]
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 (f)
Date solved : Tuesday, January 28, 2025 at 07:53:48 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+10 y^{\prime \prime }+18 y^{\prime }+9 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 27

dsolve(diff(y(x),x$4)+2*diff(y(x),x$3)+10*diff(y(x),x$2)+18*diff(y(x),x)+9*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{-x} \left (c_{2} x +c_{1} \right )+c_{3} \sin \left (3 x \right )+c_4 \cos \left (3 x \right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 38

DSolve[D[y[x],{x,4}]+2*D[y[x],{x,3}]+10*D[y[x],{x,2}]+18*D[y[x],x]+9*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (c_4 x+c_1 e^x \cos (3 x)+c_2 e^x \sin (3 x)+c_3\right ) \]