67.12.15 problem 19.3 (c)

Internal problem ID [16654]
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 : Thursday, October 02, 2025 at 01:37:23 PM
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*}

✓ Maple. Time used: 0.073 (sec). Leaf size: 25

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+26*diff(diff(y(x),x),x)+25*y(x) = 0; 
ic:=[y(0) = 6, D(y)(0) = -28, (D@@2)(y)(0) = -102, (D@@3)(y)(0) = 622]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 30

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

\begin{align*} y(x)&\to -\frac {13 \sin (x)}{4}-\frac {99}{20} \sin (5 x)+2 \cos (x)+4 \cos (5 x) \end{align*}

✓ Sympy. Time used: 0.072 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(25*y(x) + 26*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 4)),0) 
ics = {y(0): 6, Subs(Derivative(y(x), x), x, 0): -28, Subs(Derivative(y(x), (x, 2)), x, 0): -102, Subs(Derivative(y(x), (x, 3)), x, 0): 622} 
dsolve(ode,func=y(x),ics=ics)
 

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