9.2.1 problem problem 10

Internal problem ID [935]
Book : Differential equations and linear algebra, 4th ed., Edwards and Penney
Section : Section 5.3, Higher-Order Linear Differential Equations. Homogeneous Equations with Constant Coefficients. Page 300
Problem number : problem 10
Date solved : Tuesday, March 04, 2025 at 12:06:11 PM
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: 0.003 (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: 0.028 (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: 0.080 (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)
 

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