76.5.15 problem 15

Internal problem ID [17435]
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 : 15
Date solved : Tuesday, January 28, 2025 at 10:35:40 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} y^{\prime }+\frac {3 y}{t}&=t^{2} y^{2} \end{align*}

✓ Solution by Maple

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

dsolve(diff(y(t),t)+3/t*y(t)=t^2*y(t)^2,y(t), singsol=all)
 

\[ y = \frac {1}{\left (-\ln \left (t \right )+c_{1} \right ) t^{3}} \]

✓ Solution by Mathematica

Time used: 0.145 (sec). Leaf size: 23

DSolve[D[y[t],t]+3/t*y[t]==t^2*y[t]^2,y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to \frac {1}{t^3 (-\log (t)+c_1)} \\ y(t)\to 0 \\ \end{align*}