Internal problem ID [11407]
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: 26.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Bernoulli]
\[ \boxed {y^{\prime }-\frac {y^{2}+2 y t}{t^{2}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve(diff(y(t),t)=(y(t)^2+2*t*y(t))/t^2,y(t), singsol=all)
\[ y \left (t \right ) = \frac {t^{2}}{-t +c_{1}} \]
✓ Solution by Mathematica
Time used: 0.248 (sec). Leaf size: 23
DSolve[y'[t]==(y[t]^2+2*t*y[t])/t^2,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -\frac {t^2}{t-c_1} y(t)\to 0 \end{align*}