83.17.12 problem 12

Internal problem ID [19137]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter III. Ordinary linear differential equations with constant coefficients. Misc. Examples on chapter III at page 50
Problem number : 12
Date solved : Monday, March 31, 2025 at 06:49:31 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}-13 y^{\prime \prime \prime }+26 y^{\prime \prime }+82 y^{\prime }+104 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 43

ode:=diff(diff(diff(diff(diff(y(x),x),x),x),x),x)-13*diff(diff(diff(y(x),x),x),x)+26*diff(diff(y(x),x),x)+82*diff(y(x),x)+104*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-4 x} \left (\left (\sin \left (2 x \right ) c_2 +c_3 \cos \left (2 x \right )\right ) {\mathrm e}^{7 x}+\left (c_4 \sin \left (x \right )+c_5 \cos \left (x \right )\right ) {\mathrm e}^{3 x}+c_1 \right ) \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 58

ode=D[y[x],{x,5}]-13*D[y[x],{x,3}]+26*D[y[x],{x,2}]+82*D[y[x],x]+104*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-4 x} \left (c_2 e^{3 x} \cos (x)+c_4 e^{7 x} \cos (2 x)+c_1 e^{3 x} \sin (x)+c_3 e^{7 x} \sin (2 x)+c_5\right ) \]

✓ Sympy. Time used: 0.317 (sec). Leaf size: 41

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(104*y(x) + 82*Derivative(y(x), x) + 26*Derivative(y(x), (x, 2)) - 13*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 5)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{5} e^{- 4 x} + \left (C_{1} \sin {\left (x \right )} + C_{2} \cos {\left (x \right )}\right ) e^{- x} + \left (C_{3} \sin {\left (2 x \right )} + C_{4} \cos {\left (2 x \right )}\right ) e^{3 x} \]