80.3.13 problem 13

Internal problem ID [21177]
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 : 13
Date solved : Thursday, October 02, 2025 at 07:15:41 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} x \left (0\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.061 (sec). Leaf size: 13

ode:=diff(x(t),t) = 4*t^3*x(t)^(1/2); 
ic:=[x(0) = 1]; 
dsolve([ode,op(ic)],x(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.114 (sec). Leaf size: 31

ode=D[x[t],t]==4*t^3*Sqrt[x[t]]; 
ic={x[0]==1}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to \frac {1}{4} \left (t^4-2\right )^2\\ x(t)&\to \frac {1}{4} \left (t^4+2\right )^2 \end{align*}

✗ Sympy

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

NotImplementedError : Initial conditions produced too many solutions for constants