85.33.72 problem 73

Internal problem ID [22695]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 65
Problem number : 73
Date solved : Thursday, October 02, 2025 at 09:10:50 PM
CAS classification : [[_3rd_order, _quadrature]]

\begin{align*} x^{4} y^{\prime \prime \prime }+1&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 20

ode:=x^4*diff(diff(diff(y(x),x),x),x)+1 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {1}{6 x}+\frac {c_1 \,x^{2}}{2}+c_2 x +c_3 \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 25

ode=x^4*D[y[x],{x,3}]+1==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_3 x^2+\frac {1}{6 x}+c_2 x+c_1 \end{align*}

✓ Sympy. Time used: 0.203 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**4*Derivative(y(x), (x, 3)) + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} x + C_{3} x^{2} + \frac {1}{6 x} \]