73.12.2 problem 19.1 (b)

Internal problem ID [15354]
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 : 19.1 (b)
Date solved : Tuesday, January 28, 2025 at 07:53:44 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

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

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

✓ Solution by Mathematica

Time used: 60.019 (sec). Leaf size: 44

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

\[ y(x)\to \int _1^x\int _1^{K[2]}(c_1 \cos (2 K[1])+c_2 \sin (2 K[1]))dK[1]dK[2]+c_4 x+c_3 \]