74.7.20 problem 20

Internal problem ID [16097]
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 : 20
Date solved : Tuesday, January 28, 2025 at 08:39:50 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} t^{2}+t y+y^{2}-t y y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.165 (sec). Leaf size: 22

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

\[ y = t \left (-\operatorname {LambertW}\left (-\frac {{\mathrm e}^{-c_{1} -1}}{t}\right )-1\right ) \]

✓ Solution by Mathematica

Time used: 0.089 (sec). Leaf size: 30

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

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