69.15.16 problem 447

Internal problem ID [18254]
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 : 447
Date solved : Thursday, October 02, 2025 at 03:09:50 PM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 21

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

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

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

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

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

✓ Sympy. Time used: 0.093 (sec). Leaf size: 19

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

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