73.12.20 problem 19.4 (d)

Internal problem ID [15372]
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 : 19.4 (d)
Date solved : Tuesday, January 28, 2025 at 07:53:51 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+13 y^{\prime \prime }+36 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 29

dsolve(diff(y(x),x$4)+13*diff(y(x),x$2)+36*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

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

DSolve[D[y[x],{x,4}]+13*D[y[x],{x,2}]+36*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_3 \cos (2 x)+c_1 \cos (3 x)+c_4 \sin (2 x)+c_2 \sin (3 x) \]