86.8.3 problem 3

Internal problem ID [23163]
Book : An introduction to Differential Equations. By Howard Frederick Cleaves. 1969. Oliver and Boyd publisher. ISBN 0050015044
Section : Chapter 5. Linear equations of the second order with constant coefficients. Exercise 5e at page 91
Problem number : 3
Date solved : Thursday, October 02, 2025 at 09:23:38 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_y_y1]]

\begin{align*} T^{\prime \prime }+{T^{\prime }}^{3}&=0 \end{align*}

✓ Maple. Time used: 0.013 (sec). Leaf size: 31

ode:=diff(diff(T(y),y),y)+diff(T(y),y)^3 = 0; 
dsolve(ode,T(y), singsol=all);
 

\begin{align*} T &= \sqrt {2 c_1 +2 y}+c_2 \\ T &= -\sqrt {2 c_1 +2 y}+c_2 \\ \end{align*}

✓ Mathematica. Time used: 0.135 (sec). Leaf size: 41

ode=D[T[y],{y,2}]+D[T[y],y]^3==0; 
ic={}; 
DSolve[{ode,ic},T[y],y,IncludeSingularSolutions->True]
 

\begin{align*} T(y)&\to c_2-\sqrt {2 y-2 c_1}\\ T(y)&\to \sqrt {2 y-2 c_1}+c_2 \end{align*}

✓ Sympy. Time used: 3.536 (sec). Leaf size: 44

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

\[ \left [ T{\left (y \right )} = C_{1} + \sqrt {2} \sqrt {- \frac {1}{C_{2} - y}} \left (C_{2} - y\right ), \ T{\left (y \right )} = C_{1} - \sqrt {2} \sqrt {- \frac {1}{C_{2} - y}} \left (C_{2} - y\right )\right ] \]