63.4.24 problem 12

Internal problem ID [12996]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 1, First order differential equations. Section 1.3.1 Separable equations. Exercises page 26
Problem number : 12
Date solved : Monday, March 31, 2025 at 07:29:58 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Maple. Time used: 0.010 (sec). Leaf size: 5

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

\[ y = 0 \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 6

ode=D[y[t],t]==2*t*y[t]^2/(1+t^2); 
ic={y[0]==0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to 0 \]

✗ Sympy

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

ValueError : Couldnt solve for initial conditions