39.3.8 problem Problem 12.8

Internal problem ID [6534]
Book : Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill 2014
Section : Chapter 12. VARIATION OF PARAMETERS. page 104
Problem number : Problem 12.8
Date solved : Sunday, March 30, 2025 at 11:06:43 AM
CAS classification : [[_high_order, _quadrature]]

\begin{align*} y^{\prime \prime \prime \prime }&=5 x \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 35

ode:=diff(diff(diff(diff(y(x),x),x),x),x) = 5*x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x^{5}}{24}+\frac {c_1 \,x^{3}}{6}+\frac {c_2 \,x^{2}}{2}+\frac {\left (3 c_1^{2}+10 c_3 \right ) x}{10}+c_4 \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 31

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

\[ y(x)\to \frac {x^5}{24}+c_4 x^3+c_3 x^2+c_2 x+c_1 \]

✓ Sympy. Time used: 0.110 (sec). Leaf size: 22

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

\[ y{\left (x \right )} = C_{1} + C_{2} x + C_{3} x^{2} + C_{4} x^{3} + \frac {x^{5}}{24} \]