67.15.58 problem 22.12 (c)

Internal problem ID [16776]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 22. Method of undetermined coefficients. Additional exercises page 412
Problem number : 22.12 (c)
Date solved : Thursday, October 02, 2025 at 01:38:45 PM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }&=32 \,{\mathrm e}^{4 x} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 27

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-4*diff(diff(diff(y(x),x),x),x) = 32*exp(4*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (32 x +c_1 -24\right ) {\mathrm e}^{4 x}}{64}+\frac {c_2 \,x^{2}}{2}+c_3 x +c_4 \]

✓ Mathematica. Time used: 5.123 (sec). Leaf size: 100

ode=D[y[x],{x,4}]-4*D[y[x],{x,3}]==32*Exp[4*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \int _1^x\int _1^{K[3]}\int _1^{K[2]}e^{4 K[1]} (c_1+32 K[1])dK[1]dK[2]dK[3]+x (c_4 x+c_3)+c_2\\ y(x)&\to e^4 \left (-3 x^2+5 x-\frac {17}{8}\right )+\frac {1}{8} e^{4 x} (4 x-3)+x (c_4 x+c_3)+c_2 \end{align*}

✓ Sympy. Time used: 0.061 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-32*exp(4*x) - 4*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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