74.7.24 problem 24

Internal problem ID [16101]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.5, page 64
Problem number : 24
Date solved : Tuesday, January 28, 2025 at 08:40:44 AM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 35

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

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

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 38

DSolve[y[t]+(t+y[t])*D[y[t],t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{\frac {y(t)}{t}}\frac {K[1]+1}{K[1] (K[1]+2)}dK[1]=-\log (t)+c_1,y(t)\right ] \]