23.5.132 problem 132

Internal problem ID [6741]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 5. THE EQUATION IS LINEAR AND OF ORDER GREATER THAN TWO, page 410
Problem number : 132
Date solved : Tuesday, September 30, 2025 at 03:51:18 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }&=x^{3}+a^{4} y \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 38

ode:=diff(diff(diff(diff(y(x),x),x),x),x) = x^3+a^4*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {x^{3}}{a^{4}}+c_1 \cos \left (a x \right )+c_2 \,{\mathrm e}^{a x}+c_3 \sin \left (a x \right )+c_4 \,{\mathrm e}^{-a x} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 45

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

\begin{align*} y(x)&\to -\frac {x^3}{a^4}+c_2 e^{-a x}+c_4 e^{a x}+c_1 \cos (a x)+c_3 \sin (a x) \end{align*}

✓ Sympy. Time used: 0.102 (sec). Leaf size: 39

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

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