74.6.45 problem 51

Internal problem ID [16068]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.4, page 57
Problem number : 51
Date solved : Tuesday, January 28, 2025 at 08:35:11 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

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

\[ y = \frac {t^{2}}{-t +c_{1}} \]

✓ Solution by Mathematica

Time used: 0.132 (sec). Leaf size: 23

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

\begin{align*} y(t)\to -\frac {t^2}{t-c_1} \\ y(t)\to 0 \\ \end{align*}