69.15.15 problem 446

Internal problem ID [18253]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 15.2 Homogeneous differential equations with constant coefficients. Exercises page 121
Problem number : 446
Date solved : Thursday, October 02, 2025 at 03:09:50 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}+4 y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }-6 y^{\prime }-4 y&=0 \end{align*}

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

ode:=diff(diff(diff(diff(diff(y(x),x),x),x),x),x)+4*diff(diff(diff(diff(y(x),x),x),x),x)+5*diff(diff(diff(y(x),x),x),x)-6*diff(y(x),x)-4*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 44

ode=D[y[x],{x,5}]+4*D[y[x],{x,4}]+5*D[y[x],{x,3}]-6*D[y[x],x]-4*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-2 x} \left (c_4 e^x+c_5 e^{3 x}+c_2 e^x \cos (x)+c_1 e^x \sin (x)+c_3\right ) \end{align*}

✓ Sympy. Time used: 0.151 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*y(x) - 6*Derivative(y(x), x) + 5*Derivative(y(x), (x, 3)) + 4*Derivative(y(x), (x, 4)) + Derivative(y(x), (x, 5)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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