57.4.26 problem 15

Internal problem ID [14350]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 1, First order differential equations. Section 1.3.1 Separable equations. Exercises page 26
Problem number : 15
Date solved : Thursday, October 02, 2025 at 09:32:10 AM
CAS classification : [_separable]

\begin{align*} x^{\prime }&=6 t \left (x-1\right )^{{2}/{3}} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

ode:=diff(x(t),t) = 6*t*(x(t)-1)^(2/3); 
dsolve(ode,x(t), singsol=all);
 

\[ c_1 +t^{2}-\left (x-1\right )^{{1}/{3}} = 0 \]

✓ Mathematica. Time used: 0.111 (sec). Leaf size: 40

ode=D[x[t],t]==6*t*(x[t]-1)^(2/3); 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to t^6+c_1 t^4+\frac {c_1{}^2 t^2}{3}+1+\frac {c_1{}^3}{27}\\ x(t)&\to 1 \end{align*}

✓ Sympy. Time used: 0.127 (sec). Leaf size: 26

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-6*t*(x(t) - 1)**(2/3) + Derivative(x(t), t),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = \frac {C_{1}^{3}}{27} + \frac {C_{1}^{2} t^{2}}{3} + C_{1} t^{4} + t^{6} + 1 \]