73.12.3 problem 19.1 (c)

Internal problem ID [15355]
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 (c)
Date solved : Tuesday, January 28, 2025 at 07:53:44 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-34 y^{\prime \prime }+225 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 29

dsolve(diff(y(x),x$4)-34*diff(y(x),x$2)+225*y(x)=0,y(x), singsol=all)
 

\[ y = \left (c_{2} {\mathrm e}^{10 x}+c_{3} {\mathrm e}^{8 x}+{\mathrm e}^{2 x} c_{1} +c_4 \right ) {\mathrm e}^{-5 x} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 39

DSolve[D[y[x],{x,4}]-34*D[y[x],{x,2}]+225*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-5 x} \left (e^{2 x} \left (c_3 e^{6 x}+c_4 e^{8 x}+c_2\right )+c_1\right ) \]