76.5.13 problem 13

Internal problem ID [17433]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.7 (Substitution Methods). Problems at page 108
Problem number : 13
Date solved : Tuesday, January 28, 2025 at 10:35:36 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Solution by Maple

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

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

\[ y = \frac {1}{\left (-t +c_{1} \right ) t} \]

✓ Solution by Mathematica

Time used: 0.153 (sec). Leaf size: 23

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

\begin{align*} y(t)\to -\frac {1}{t^2-c_1 t} \\ y(t)\to 0 \\ \end{align*}