73.15.59 problem 22.12 (d)

Internal problem ID [15419]
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 (d)
Date solved : Monday, March 31, 2025 at 01:37:08 PM
CAS classification : [[_high_order, _missing_y]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 32

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

\[ y = -\frac {x^{4}}{3}-\frac {x^{3}}{3}+\frac {c_2 \,x^{2}}{2}+\frac {{\mathrm e}^{4 x} c_1}{64}+c_3 x +c_4 \]

✓ Mathematica. Time used: 26.837 (sec). Leaf size: 68

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

\[ y(x)\to \int _1^x\int _1^{K[4]}\int _1^{K[3]}e^{4 K[2]} \left (c_1+\int _1^{K[2]}32 e^{-4 K[1]} K[1]dK[1]\right )dK[2]dK[3]dK[4]+x (c_4 x+c_3)+c_2 \]

✓ Sympy. Time used: 0.096 (sec). Leaf size: 29

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

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