75.15.11 problem 442

Internal problem ID [16891]
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 : 442
Date solved : Monday, March 31, 2025 at 03:34:50 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+10 y^{\prime \prime }+12 y^{\prime }+5 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 26

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+4*diff(diff(diff(y(x),x),x),x)+10*diff(diff(y(x),x),x)+12*diff(y(x),x)+5*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 32

ode=D[y[x],{x,4}]+4*D[y[x],{x,3}]+10*D[y[x],{x,2}]+12*D[y[x],x]+5*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-x} (c_4 x+c_2 \cos (2 x)+c_1 \sin (2 x)+c_3) \]

✓ Sympy. Time used: 0.195 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(5*y(x) + 12*Derivative(y(x), x) + 10*Derivative(y(x), (x, 2)) + 4*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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