63.4.30 problem 26

Internal problem ID [13073]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 1, First order differential equations. Section 1.3.1 Separable equations. Exercises page 26
Problem number : 26
Date solved : Tuesday, January 28, 2025 at 04:51:23 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.157 (sec). Leaf size: 23

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

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