73.12.15 problem 19.3 (c)

Internal problem ID [15367]
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 : 19.3 (c)
Date solved : Tuesday, January 28, 2025 at 07:53:49 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+26 y^{\prime \prime }+25 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=6\\ y^{\prime }\left (0\right )&=-28\\ y^{\prime \prime }\left (0\right )&=-102\\ y^{\prime \prime \prime }\left (0\right )&=622 \end{align*}

✓ Solution by Maple

Time used: 0.084 (sec). Leaf size: 25

dsolve([diff(y(x),x$4)+26*diff(y(x),x$2)+25*y(x)=0,y(0) = 6, D(y)(0) = -28, (D@@2)(y)(0) = -102, (D@@3)(y)(0) = 622],y(x), singsol=all)
 

\[ y = -\frac {99 \sin \left (5 x \right )}{20}+4 \cos \left (5 x \right )-\frac {13 \sin \left (x \right )}{4}+2 \cos \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 30

DSolve[{D[y[x],{x,4}]+26*D[y[x],{x,2}]+25*y[x]==0,{y[0]==6,Derivative[1][y][0] ==-28,Derivative[2][y][0] ==-102,Derivative[3][y][0]==622}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {13 \sin (x)}{4}-\frac {99}{20} \sin (5 x)+2 \cos (x)+4 \cos (5 x) \]