Internal problem ID [14336]
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: 53.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {5 t y+4 y^{2}+\left (t^{2}+2 t y\right ) y^{\prime }=-1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 59
dsolve((5*t*y(t)+4*y(t)^2+1)+(t^2+2*t*y(t))*diff(y(t),t)=0,y(t), singsol=all)
\begin{align*} y \left (t \right ) &= \frac {-t^{3}-\sqrt {t^{6}-t^{4}-4 c_{1}}}{2 t^{2}} \\ y \left (t \right ) &= \frac {-t^{3}+\sqrt {t^{6}-t^{4}-4 c_{1}}}{2 t^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.611 (sec). Leaf size: 84
DSolve[(5*t*y[t]+4*y[t]^2+1)+(t^2+2*t*y[t])*y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -\frac {t^5+\sqrt {t^3} \sqrt {t^7-t^5+4 c_1 t}}{2 t^4} \\ y(t)\to -\frac {t}{2}+\frac {\sqrt {t^3} \sqrt {t^7-t^5+4 c_1 t}}{2 t^4} \\ \end{align*}