80.2.12 problem 17

Internal problem ID [21155]
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 2. Theory of first order differential equations. Excercise 2.6 at page 37
Problem number : 17
Date solved : Thursday, October 02, 2025 at 07:11:13 PM
CAS classification : [_Chini]

\begin{align*} x^{\prime }&=t^{2} x^{4}+1 \end{align*}

With initial conditions

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

ode=D[x[t],t]==t^2*x[t]^4+1; 
ic={x[0]==0}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-t**2*x(t)**4 + Derivative(x(t), t) + 1,0) 
ics = {x(0): 0} 
dsolve(ode,func=x(t),ics=ics)
 

NotImplementedError : The given ODE -t**2*x(t)**4 + Derivative(x(t), t) + 1 cannot be solved by the lie group method