Internal problem ID [14337]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.4, page 57
Problem number: 54.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class D`], _rational, _Bernoulli]
\[ \boxed {5 t y^{2}+y+\left (2 t^{3}-t \right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 23
dsolve((5*t*y(t)^2+y(t))+(2*t^3-t)*diff(y(t),t)=0,y(t), singsol=all)
\[ y \left (t \right ) = \frac {2 t}{-5+2 \sqrt {2 t^{2}-1}\, c_{1}} \]
✓ Solution by Mathematica
Time used: 0.196 (sec). Leaf size: 32
DSolve[(5*t*y[t]^2+y[t])+(2*t^3-t)*y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {2 t}{-5+2 c_1 \sqrt {1-2 t^2}} \\ y(t)\to 0 \\ \end{align*}