87.2.8 problem 8

Internal problem ID [23243]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 1. Elementary methods. First order differential equations. Exercise at page 17
Problem number : 8
Date solved : Thursday, October 02, 2025 at 09:25:13 PM
CAS classification : [_separable]

\begin{align*} x^{\prime }&=\frac {a x^{{5}/{6}}}{\left (-B t +b \right )^{{3}/{2}}} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 25

ode:=diff(x(t),t) = a*x(t)^(5/6)/(-B*t+b)^(3/2); 
dsolve(ode,x(t), singsol=all);
 

\[ x^{{1}/{6}}-\frac {a}{3 B \sqrt {-B t +b}}-c_1 = 0 \]

✓ Mathematica. Time used: 0.159 (sec). Leaf size: 157

ode=D[x[t],t]== a*x[t]^(5/6)/(b-B*t)^(3/2); 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to \frac {64 a^6 \sqrt {b-B t}+192 a^5 B c_1 (b-B t)+240 a^4 B^2 c_1{}^2 (b-B t)^{3/2}+160 a^3 B^3 c_1{}^3 (b-B t)^2+60 a^2 B^4 c_1{}^4 (b-B t)^{5/2}+12 a B^5 c_1{}^5 (b-B t)^3+B^6 c_1{}^6 (b-B t)^{7/2}}{46656 B^6 (b-B t)^{7/2}}\\ x(t)&\to 0 \end{align*}

✗ Sympy

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-a*x(t)**(5/6)/(-B*t + b)**(3/2) + Derivative(x(t), t),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

Timed Out