74.8.11 problem 11

Internal problem ID [16076]
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 : 11
Date solved : Monday, March 31, 2025 at 02:38:57 PM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.016 (sec). Leaf size: 51

ode:=y(t)-t+(t+y(t))*diff(y(t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\begin{align*} y &= \frac {-t c_1 -\sqrt {2 t^{2} c_1^{2}+1}}{c_1} \\ y &= \frac {-t c_1 +\sqrt {2 t^{2} c_1^{2}+1}}{c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.448 (sec). Leaf size: 94

ode=(y[t]-t)+(t+y[t])*D[y[t],t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)\to -t-\sqrt {2 t^2+e^{2 c_1}} \\ y(t)\to -t+\sqrt {2 t^2+e^{2 c_1}} \\ y(t)\to -\sqrt {2} \sqrt {t^2}-t \\ y(t)\to \sqrt {2} \sqrt {t^2}-t \\ \end{align*}

✓ Sympy. Time used: 1.043 (sec). Leaf size: 29

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

\[ \left [ y{\left (t \right )} = - t - \sqrt {C_{1} + 2 t^{2}}, \ y{\left (t \right )} = - t + \sqrt {C_{1} + 2 t^{2}}\right ] \]