63.4.24 problem 12

Internal problem ID [13067]
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 : Tuesday, January 28, 2025 at 04:51:06 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*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 5

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

\[ y = 0 \]

✓ Solution by Mathematica

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

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

\[ y(t)\to 0 \]