70.3.10 problem 10

Internal problem ID [18668]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.4 (Differences between linear and nonlinear equations). Problems at page 79
Problem number : 10
Date solved : Thursday, October 02, 2025 at 03:19:29 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} y^{\prime }&=\left (t^{2}+y^{2}\right )^{{3}/{2}} \end{align*}

✗ Maple

ode:=diff(y(t),t) = (t^2+y(t)^2)^(3/2); 
dsolve(ode,y(t), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[t],t]==(t^2+y[t]^2)^(3/2); 
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 + y(t)**2)**(3/2) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

NotImplementedError : The given ODE -(t**2 + y(t)**2)**(3/2) + Derivative(y(t), t) cannot be solved by the lie group method