5.2.11 problem 18

Internal problem ID [1482]
Book : Elementary differential equations and boundary value problems, 11th ed., Boyce, DiPrima, Meade
Section : Chapter 4.2, Higher order linear differential equations. Constant coefficients. page 180
Problem number : 18
Date solved : Tuesday, September 30, 2025 at 04:34:32 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-7 y^{\prime \prime \prime }+6 y^{\prime \prime }+30 y^{\prime }-36 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 38

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-7*diff(diff(diff(y(x),x),x),x)+6*diff(diff(y(x),x),x)+30*diff(y(x),x)-36*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{-2 x}+c_2 \,{\mathrm e}^{3 x}+c_3 \,{\mathrm e}^{\left (3+\sqrt {3}\right ) x}+c_4 \,{\mathrm e}^{-\left (-3+\sqrt {3}\right ) x} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 51

ode=D[y[x],{x,4}]-7*D[y[x],{x,3}]+6*D[y[x],{x,2}]+30*D[y[x],x]-36*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 e^{-\left (\left (\sqrt {3}-3\right ) x\right )}+c_2 e^{\left (3+\sqrt {3}\right ) x}+c_3 e^{-2 x}+c_4 e^{3 x} \end{align*}

✓ Sympy. Time used: 0.175 (sec). Leaf size: 36

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-36*y(x) + 30*Derivative(y(x), x) + 6*Derivative(y(x), (x, 2)) - 7*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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