40.8.2 problem 17

Internal problem ID [6702]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 13. Homogeneous Linear equations with constant coefficients. Supplemetary problems. Page 86
Problem number : 17
Date solved : Wednesday, March 05, 2025 at 02:39:42 AM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 23

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

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

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 25

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

\[ y(x)\to -\frac {1}{2} c_1 e^{-2 x}+c_2 e^x+c_3 \]

✓ Sympy. Time used: 0.245 (sec). Leaf size: 15

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

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