Internal problem ID [14310]
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: 22.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {3 t^{2} y+3 y^{2}+\left (t^{3}+6 t y\right ) y^{\prime }=1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 59
dsolve((3*t^2*y(t)+3*y(t)^2-1)+(t^3+6*t*y(t))*diff(y(t),t)=0,y(t), singsol=all)
\begin{align*} y \left (t \right ) &= \frac {-t^{3}+\sqrt {t \left (t^{5}-12 c_{1} +12 t \right )}}{6 t} \\ y \left (t \right ) &= \frac {-t^{3}-\sqrt {t \left (t^{5}-12 c_{1} +12 t \right )}}{6 t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.462 (sec). Leaf size: 67
DSolve[(3*t^2*y[t]+3*y[t]^2-1)+(t^3+6*t*y[t])*y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -\frac {t^3+\sqrt {t \left (t^5+12 t+36 c_1\right )}}{6 t} \\ y(t)\to \frac {-t^3+\sqrt {t \left (t^5+12 t+36 c_1\right )}}{6 t} \\ \end{align*}