87.12.8 problem 8

Internal problem ID [23456]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 93
Problem number : 8
Date solved : Thursday, October 02, 2025 at 09:41:58 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-7 y^{\prime \prime }+5 y^{\prime }+y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 30

ode:=diff(diff(diff(y(x),x),x),x)-7*diff(diff(y(x),x),x)+5*diff(y(x),x)+y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{x}+c_2 \,{\mathrm e}^{\left (3+\sqrt {10}\right ) x}+c_3 \,{\mathrm e}^{-\left (-3+\sqrt {10}\right ) x} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 41

ode=D[y[x],{x,3}]-7*D[y[x],{x,2}]+5*D[y[x],{x,1}]+y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 e^{-\left (\left (\sqrt {10}-3\right ) x\right )}+c_2 e^{\left (3+\sqrt {10}\right ) x}+c_3 e^x \end{align*}

✓ Sympy. Time used: 0.191 (sec). Leaf size: 32

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) + 5*Derivative(y(x), x) - 7*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} + \left (C_{2} e^{- \sqrt {10} x} + C_{3} e^{\sqrt {10} x}\right ) e^{2 x}\right ) e^{x} \]