74.3.2 problem 1 (b)

Internal problem ID [15791]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.1, page 32
Problem number : 1 (b)
Date solved : Monday, March 31, 2025 at 01:49:31 PM
CAS classification : [_rational]

\begin{align*} y^{\prime }+t^{2}&=\frac {1}{y^{2}} \end{align*}

✗ Maple

ode:=diff(y(t),t)+t^2 = 1/y(t)^2; 
dsolve(ode,y(t), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[t],t]+t^2==1/y[t]^2; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

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

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