74.7.29 problem 29

Internal problem ID [16027]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.5, page 64
Problem number : 29
Date solved : Thursday, March 13, 2025 at 07:19:52 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 37

ode:=(t^2-y(t)^2)*diff(y(t),t)+y(t)^2+t*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\begin{align*} y &= -t \\ y &= t -\sqrt {t^{2}-2 c_{1}} \\ y &= t +\sqrt {t^{2}-2 c_{1}} \\ \end{align*}

✓ Mathematica. Time used: 0.093 (sec). Leaf size: 46

ode=(t^2-y[t]^2)*D[y[t],t]+(y[t]^2+t*y[t])==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)\to -t \\ \text {Solve}\left [\int _1^{\frac {y(t)}{t}}\frac {K[1]-1}{(K[1]-2) K[1]}dK[1]&=-\log (t)+c_1,y(t)\right ] \\ \end{align*}

✓ Sympy. Time used: 1.189 (sec). Leaf size: 29

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

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