69.15.17 problem 448

Internal problem ID [18255]
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 : 448
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 }+2 y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 18

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

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

✓ Mathematica. Time used: 60.023 (sec). Leaf size: 33

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

\begin{align*} y(x)&\to \int _1^xe^{K[1]} (c_2 \cos (K[1])+c_1 \sin (K[1]))dK[1]+c_3 \end{align*}

✓ Sympy. Time used: 0.086 (sec). Leaf size: 17

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

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