Internal problem ID [14335]
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: 52.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type
[_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class B`]]
\[ \boxed {y+\left (t^{2} y-t \right ) y^{\prime }=-2 t^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 51
dsolve((y(t)+2*t^2)+(t^2*y(t)-t)*diff(y(t),t)=0,y(t), singsol=all)
\begin{align*} y \left (t \right ) &= \frac {1+\sqrt {-2 c_{1} t^{2}-4 t^{3}+1}}{t} \\ y \left (t \right ) &= \frac {1-\sqrt {-2 c_{1} t^{2}-4 t^{3}+1}}{t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.47 (sec). Leaf size: 68
DSolve[(y[t]+2*t^2)+(t^2*y[t]-t)*y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{t}-\sqrt {\frac {1}{t^2}} \sqrt {-4 t^3+c_1 t^2+1} \\ y(t)\to \frac {1}{t}+\sqrt {\frac {1}{t^2}} \sqrt {-4 t^3+c_1 t^2+1} \\ \end{align*}