85.28.4 problem 4

Internal problem ID [22611]
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. B Exercises at page 60
Problem number : 4
Date solved : Thursday, October 02, 2025 at 08:55:01 PM
CAS classification : [[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]

\begin{align*} {y^{\prime \prime \prime }}^{2}&={y^{\prime \prime }}^{3} \end{align*}

✓ Maple. Time used: 0.097 (sec). Leaf size: 23

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

\begin{align*} y &= c_1 x +c_2 \\ y &= -4 \ln \left (c_1 +x \right )+c_2 x +c_3 \\ \end{align*}

✓ Mathematica. Time used: 0.097 (sec). Leaf size: 39

ode=D[y[x],{x,3}]^2==D[y[x],{x,2}]^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_3 x-4 \log (x-c_1)+c_2\\ y(x)&\to c_3 x-4 \log (x+c_1)+c_2 \end{align*}

✓ Sympy. Time used: 0.544 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-Derivative(y(x), (x, 2))**3 + Derivative(y(x), (x, 3))**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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