74.8.16 problem 16

Internal problem ID [16152]
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
Date solved : Tuesday, January 28, 2025 at 08:52:50 AM
CAS classification : [_exact, _rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 47

dsolve((t^2-y(t))+(y(t)-t)*diff(y(t),t)=0,y(t), singsol=all)
 

\begin{align*} y &= t -\frac {\sqrt {-6 t^{3}+9 t^{2}-18 c_{1}}}{3} \\ y &= 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)*D[y[t],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*}