63.4.30 problem 26

Internal problem ID [12994]
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 : Wednesday, March 05, 2025 at 08:56:37 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

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

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

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

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

ode=D[y[t],t]==(y[t]^2+2*t*y[t])/t^2; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.211 (sec). Leaf size: 8

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(Derivative(y(t), t) - (2*t*y(t) + y(t)**2)/t**2,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {t^{2}}{C_{1} - t} \]