74.6.48 problem 54

Internal problem ID [16071]
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 : 54
Date solved : Tuesday, January 28, 2025 at 08:35:17 AM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

\begin{align*} 5 t y^{2}+y+\left (2 t^{3}-t \right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

dsolve((5*t*y(t)^2+y(t))+(2*t^3-t)*diff(y(t),t)=0,y(t), singsol=all)
 

\[ y = \frac {2 t}{-5+2 \sqrt {2 t^{2}-1}\, c_{1}} \]

✓ Solution by Mathematica

Time used: 0.491 (sec). Leaf size: 78

DSolve[(5*t*y[t]^2+y[t])+(2*t^3-t)*D[y[t],t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to \frac {\exp \left (\int _1^t\frac {1}{K[1]-2 K[1]^3}dK[1]\right )}{-\int _1^t\frac {5 \exp \left (\int _1^{K[2]}\frac {1}{K[1]-2 K[1]^3}dK[1]\right )}{1-2 K[2]^2}dK[2]+c_1} \\ y(t)\to 0 \\ \end{align*}