68.8.16 problem 16

Internal problem ID [17439]
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 : Thursday, October 02, 2025 at 02:22:08 PM
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*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 47

ode:=t^2-y(t)+(-t+y(t))*diff(y(t),t) = 0; 
dsolve(ode,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*}

✓ Mathematica. Time used: 0.094 (sec). Leaf size: 63

ode=(t^2-y[t])+(y[t]-t)*D[y[t],t]==0; 
ic={}; 
DSolve[{ode,ic},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*}

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t**2 + (-t + y(t))*Derivative(y(t), t) - y(t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

Timed Out