7.10.10 problem 10

Internal problem ID [280]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.3 (Homogeneous equations with constant coefficients). Problems at page 134
Problem number : 10
Date solved : Tuesday, March 04, 2025 at 11:07:10 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} 5 y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 20

ode:=5*diff(diff(diff(diff(y(x),x),x),x),x)+3*diff(diff(diff(y(x),x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 +c_2 x +c_3 \,x^{2}+c_4 \,{\mathrm e}^{-\frac {3 x}{5}} \]

✓ Mathematica. Time used: 0.041 (sec). Leaf size: 30

ode=5*D[y[x],{x,4}]+3*D[y[x],{x,3}]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -\frac {125}{27} c_1 e^{-3 x/5}+x (c_4 x+c_3)+c_2 \]

✓ Sympy. Time used: 0.093 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*Derivative(y(x), (x, 3)) + 5*Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} x + C_{3} x^{2} + C_{4} e^{- \frac {3 x}{5}} \]