67.8.19 problem 13.3 (d)

Internal problem ID [16514]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 13. Higher order equations: Extending first order concepts. Additional exercises page 259
Problem number : 13.3 (d)
Date solved : Thursday, October 02, 2025 at 01:35:53 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }&=-2 y^{\prime \prime \prime } \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 20

ode:=diff(diff(diff(diff(y(x),x),x),x),x) = -2*diff(diff(diff(y(x),x),x),x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 28

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

\begin{align*} y(x)&\to -\frac {1}{8} c_1 e^{-2 x}+x (c_4 x+c_3)+c_2 \end{align*}

✓ Sympy. Time used: 0.045 (sec). Leaf size: 19

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

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