73.12.24 problem 19.4 (h)

Internal problem ID [15376]
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 (h)
Date solved : Tuesday, January 28, 2025 at 07:53:53 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime \prime \prime }+15 y^{\prime \prime }-4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 29

dsolve(4*diff(y(x),x$4)+15*diff(y(x),x$2)-4*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 37

DSolve[4*D[y[x],{x,4}]+15*D[y[x],{x,2}]-4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x/2} \left (c_4 e^x+c_3\right )+c_1 \cos (2 x)+c_2 \sin (2 x) \]