74.1.23 problem 30

Internal problem ID [15803]
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
Date solved : Tuesday, January 28, 2025 at 08:07:45 AM
CAS classification : [[_homogeneous, `class G`], _exact, _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} 3 y \left (t^{2}+y\right )+t \left (t^{2}+6 y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.193 (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 &= \frac {-t^{3}+\sqrt {t \left (t^{5}+12 c_{1} \right )}}{6 t} \\ y &= \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])*D[y[x],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*}