80.3.10 problem 10

Internal problem ID [21174]
Book : A Textbook on Ordinary Differential Equations by Shair Ahmad and Antonio Ambrosetti. Second edition. ISBN 978-3-319-16407-6. Springer 2015
Section : Chapter 3. First order nonlinear differential equations. Excercise 3.7 at page 67
Problem number : 10
Date solved : Thursday, October 02, 2025 at 07:15:31 PM
CAS classification : [_separable]

\begin{align*} x^{\prime }&=-\frac {t}{4 x^{3}} \end{align*}

With initial conditions

\begin{align*} x \left (1\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.060 (sec). Leaf size: 17

ode:=diff(x(t),t) = -1/4*t/x(t)^3; 
ic:=[x(1) = 1]; 
dsolve([ode,op(ic)],x(t), singsol=all);
 

\[ x = \left (\frac {1}{2}-\frac {i}{2}\right ) \left (2 t^{2}-6\right )^{{1}/{4}} \]

✓ Mathematica. Time used: 0.181 (sec). Leaf size: 22

ode=D[x[t],t]==-t/(4*x[t]^3); 
ic={x[1]==1}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to \frac {\sqrt [4]{3-t^2}}{\sqrt [4]{2}} \end{align*}

✓ Sympy. Time used: 0.561 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(t/(4*x(t)**3) + Derivative(x(t), t),0) 
ics = {x(1): 1} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = \sqrt [4]{\frac {3}{2} - \frac {t^{2}}{2}} \]