74.8.13 problem 13

Internal problem ID [16149]
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 : 13
Date solved : Tuesday, January 28, 2025 at 08:52:11 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.294 (sec). Leaf size: 45

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

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

✓ Solution by Mathematica

Time used: 0.118 (sec). Leaf size: 40

DSolve[y[t]^2+(t*y[t]+t^2)*D[y[t],t]==0,y[t],t,IncludeSingularSolutions -> True]
 

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