Internal problem ID [11401]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\frac {2 t y^{2}}{t^{2}+1}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 5
dsolve([diff(y(t),t)=2*t*y(t)^2/(1+t^2),y(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = 0 \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 6
DSolve[{y'[t]==2*t*y[t]^2/(1+t^2),{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to 0 \]