69.15.14 problem 445

Internal problem ID [18252]
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 : 445
Date solved : Thursday, October 02, 2025 at 03:09:49 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+4 y^{\prime \prime }-2 y^{\prime }-5 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 28

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+2*diff(diff(diff(y(x),x),x),x)+4*diff(diff(y(x),x),x)-2*diff(y(x),x)-5*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 36

ode=D[y[x],{x,4}]+2*D[y[x],{x,3}]+4*D[y[x],{x,2}]-2*D[y[x],x]-5*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.128 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-5*y(x) - 2*Derivative(y(x), x) + 4*Derivative(y(x), (x, 2)) + 2*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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