Internal problem ID [14418]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Review exercises, page 80
Problem number: 16.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type
[_exact, _rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]
\[ \boxed {-y+\left (-t +y\right ) y^{\prime }=-t^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 47
dsolve((t^2-y(t))+(y(t)-t)*diff(y(t),t)=0,y(t), singsol=all)
\begin{align*} y \left (t \right ) &= t -\frac {\sqrt {-6 t^{3}+9 t^{2}-18 c_{1}}}{3} \\ y \left (t \right ) &= t +\frac {\sqrt {-6 t^{3}+9 t^{2}-18 c_{1}}}{3} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.143 (sec). Leaf size: 63
DSolve[(t^2-y[t])+(y[t]-t)*y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to t-i \sqrt {\frac {2 t^3}{3}-t^2-c_1} \\ y(t)\to t+i \sqrt {\frac {2 t^3}{3}-t^2-c_1} \\ \end{align*}