Internal problem ID [14362]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.5, page 64
Problem number: 19.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {t y-y^{2}+t \left (t -3 y\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 1.063 (sec). Leaf size: 239
dsolve(( t*y(t)-y(t)^2 )+( t*(t-3*y(t)) )*diff(y(t),t)=0,y(t), singsol=all)
\begin{align*} y \left (t \right ) &= \frac {{\left (\left (\sqrt {3}\, \sqrt {c_{1}^{4} t^{4}+27}+9\right ) t c_{1} \right )}^{\frac {1}{3}} 3^{\frac {2}{3}}}{c_{1} \left (-t^{2} c_{1}^{2} 3^{\frac {1}{3}}+{\left (\left (\sqrt {3}\, \sqrt {c_{1}^{4} t^{4}+27}+9\right ) t c_{1} \right )}^{\frac {2}{3}}\right )} \\ y \left (t \right ) &= -\frac {2 {\left (\left (\sqrt {3}\, \sqrt {c_{1}^{4} t^{4}+27}+9\right ) t c_{1} \right )}^{\frac {1}{3}} 3^{\frac {2}{3}}}{\left (\left (1+i \sqrt {3}\right ) {\left (\left (\sqrt {3}\, \sqrt {c_{1}^{4} t^{4}+27}+9\right ) t c_{1} \right )}^{\frac {2}{3}}+c_{1}^{2} t^{2} \left (i 3^{\frac {5}{6}}-3^{\frac {1}{3}}\right )\right ) c_{1}} \\ y \left (t \right ) &= \frac {2 {\left (\left (\sqrt {3}\, \sqrt {c_{1}^{4} t^{4}+27}+9\right ) t c_{1} \right )}^{\frac {1}{3}} 3^{\frac {2}{3}}}{\left (\left (i \sqrt {3}-1\right ) {\left (\left (\sqrt {3}\, \sqrt {c_{1}^{4} t^{4}+27}+9\right ) t c_{1} \right )}^{\frac {2}{3}}+\left (i 3^{\frac {5}{6}}+3^{\frac {1}{3}}\right ) c_{1}^{2} t^{2}\right ) c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 60.223 (sec). Leaf size: 373
DSolve[( t*y[t]-y[t]^2 )+( t*(t-3*y[t]) )*y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{6} \left (\sqrt [3]{\frac {t^4+6 \sqrt {81 e^{4 c_1}-3 e^{2 c_1} t^4}-54 e^{2 c_1}}{t}}+\frac {t^2}{\sqrt [3]{\frac {t^4+6 \sqrt {81 e^{4 c_1}-3 e^{2 c_1} t^4}-54 e^{2 c_1}}{t}}}+t\right ) \\ y(t)\to \frac {1}{12} \left (i \left (\sqrt {3}+i\right ) \sqrt [3]{\frac {t^4+6 \sqrt {81 e^{4 c_1}-3 e^{2 c_1} t^4}-54 e^{2 c_1}}{t}}-\frac {i \left (\sqrt {3}-i\right ) t^2}{\sqrt [3]{\frac {t^4+6 \sqrt {81 e^{4 c_1}-3 e^{2 c_1} t^4}-54 e^{2 c_1}}{t}}}+2 t\right ) \\ y(t)\to \frac {1}{12} \left (-\left (1+i \sqrt {3}\right ) \sqrt [3]{\frac {t^4+6 \sqrt {81 e^{4 c_1}-3 e^{2 c_1} t^4}-54 e^{2 c_1}}{t}}+\frac {i \left (\sqrt {3}+i\right ) t^2}{\sqrt [3]{\frac {t^4+6 \sqrt {81 e^{4 c_1}-3 e^{2 c_1} t^4}-54 e^{2 c_1}}{t}}}+2 t\right ) \\ \end{align*}