40.9.4 problem 14

Internal problem ID [6714]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 14. Linear equations with constant coefficients. Supplemetary problems. Page 92
Problem number : 14
Date solved : Sunday, March 30, 2025 at 11:20:26 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}-4 y^{\prime \prime \prime }&=5 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 34

ode:=diff(diff(diff(diff(diff(y(x),x),x),x),x),x)-4*diff(diff(diff(y(x),x),x),x) = 5; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {5 x^{3}}{24}+\frac {c_3 \,x^{2}}{2}-\frac {{\mathrm e}^{-2 x} c_1}{8}+\frac {{\mathrm e}^{2 x} c_2}{8}+c_4 x +c_5 \]

✓ Mathematica. Time used: 0.081 (sec). Leaf size: 47

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

\[ y(x)\to -\frac {5 x^3}{24}+c_5 x^2+c_4 x+\frac {1}{8} c_1 e^{2 x}-\frac {1}{8} c_2 e^{-2 x}+c_3 \]

✓ Sympy. Time used: 0.144 (sec). Leaf size: 32

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

\[ y{\left (x \right )} = C_{1} + C_{2} x + C_{3} x^{2} + C_{4} e^{- 2 x} + C_{5} e^{2 x} - \frac {5 x^{3}}{24} \]