85.27.7 problem 7

Internal problem ID [22599]
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 60
Problem number : 7
Date solved : Thursday, October 02, 2025 at 08:54:51 PM
CAS classification : [[_3rd_order, _quadrature]]

\begin{align*} x^{3} y^{\prime \prime \prime }&=1+\sqrt {x} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 24

ode:=x^3*diff(diff(diff(y(x),x),x),x) = 1+x^(1/2); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\ln \left (x \right )}{2}+\frac {8 \sqrt {x}}{3}+\frac {c_1 \,x^{2}}{2}+c_2 x +c_3 \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 33

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

\begin{align*} y(x)&\to c_3 x^2+\frac {8 \sqrt {x}}{3}+\frac {\log (x)}{2}+c_2 x+c_1 \end{align*}

✓ Sympy. Time used: 0.209 (sec). Leaf size: 26

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

\[ y{\left (x \right )} = C_{1} + C_{2} x + C_{3} x^{2} + \frac {8 \sqrt {x}}{3} + \frac {\log {\left (x \right )}}{2} \]