74.7.7 problem 7

Internal problem ID [16084]
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 : 7
Date solved : Tuesday, January 28, 2025 at 08:38:35 AM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 16

dsolve(diff(y(t),t)-1/t*y(t)=t*y(t)^2,y(t), singsol=all)
 

\[ y = -\frac {3 t}{t^{3}-3 c_{1}} \]

✓ Solution by Mathematica

Time used: 0.135 (sec). Leaf size: 23

DSolve[D[y[t],t]-1/t*y[t]==t*y[t]^2,y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to -\frac {3 t}{t^3-3 c_1} \\ y(t)\to 0 \\ \end{align*}