74.8.11 problem 11

Internal problem ID [16147]
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 : Tuesday, January 28, 2025 at 08:52:05 AM
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*}

✓ Solution by Maple

Time used: 0.143 (sec). Leaf size: 51

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

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

✓ Solution by Mathematica

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

DSolve[(y[t]-t)+(t+y[t])*D[y[t],t]==0,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*}