Internal problem ID [14067]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number: 30.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _exact, _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {3 y \left (t^{2}+y\right )+t \left (t^{2}+6 y\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 53
dsolve(3*y(t)*(t^2+y(t))+t*(t^2+6*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} \right )}}{6 t} \\ y \left (t \right ) &= \frac {-t^{3}-\sqrt {t \left (t^{5}+12 c_{1} \right )}}{6 t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 114
DSolve[3*y[t]*(t^2+y[t])+t*(t^2+6*y[t])*y'[x]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{6} \left (-\sqrt {3} \sqrt {t^2 \left (3 t^2+8 t y'(x)+12 y'(x)^2\right )}-3 t^2-6 t y'(x)\right ) \\ y(t)\to \frac {1}{6} \left (\sqrt {3} \sqrt {t^2 \left (3 t^2+8 t y'(x)+12 y'(x)^2\right )}-3 t^2-6 t y'(x)\right ) \\ \end{align*}