9.10.8 problem 8

Internal problem ID [3095]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 18, page 82
Problem number : 8
Date solved : Tuesday, September 30, 2025 at 06:27:01 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} 4 y^{\left (5\right )}-3 y^{\prime \prime \prime }-y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 23

ode:=4*diff(diff(diff(diff(diff(y(x),x),x),x),x),x)-3*diff(diff(diff(y(x),x),x),x)-diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_5 x +c_4 \right ) {\mathrm e}^{-\frac {x}{2}}+c_2 x +c_3 \,{\mathrm e}^{x}+c_1 \]

✓ Mathematica. Time used: 0.049 (sec). Leaf size: 36

ode=4*D[y[x],{x,5}]-3*D[y[x],{x,3}]-D[y[x],{x,2}]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 4 e^{-x/2} (c_2 (x+4)+c_1)+c_3 e^x+c_5 x+c_4 \end{align*}

✓ Sympy. Time used: 0.064 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-Derivative(y(x), (x, 2)) - 3*Derivative(y(x), (x, 3)) + 4*Derivative(y(x), (x, 5)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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