Internal problem ID [11437]
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 1.4.1. Integrating factors. Exercises
page 41
Problem number: 15(d).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Bernoulli]
\[ \boxed {t^{2} y^{\prime }+2 y t -y^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(t^2*diff(y(t),t)+2*t*y(t)-y(t)^2=0,y(t), singsol=all)
\[ y \left (t \right ) = \frac {3 t}{3 c_{1} t^{3}+1} \]
✓ Solution by Mathematica
Time used: 0.246 (sec). Leaf size: 24
DSolve[t^2*y'[t]+2*t*y[t]-y[t]^2==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {3 t}{1+3 c_1 t^3} y(t)\to 0 \end{align*}