74.6.16 problem 17

Internal problem ID [15968]
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 : 17
Date solved : Monday, March 31, 2025 at 02:16:59 PM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, _dAlembert]

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

✓ Maple. Time used: 0.017 (sec). Leaf size: 205

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

\begin{align*} y &= -\frac {2 \left (t^{2} c_1 -\frac {\left (4+4 \sqrt {4 t^{6} c_1^{3}+1}\right )^{{2}/{3}}}{4}\right )}{\left (4+4 \sqrt {4 t^{6} c_1^{3}+1}\right )^{{1}/{3}} \sqrt {c_1}} \\ y &= -\frac {\left (1+i \sqrt {3}\right ) \left (4+4 \sqrt {4 t^{6} c_1^{3}+1}\right )^{{1}/{3}}}{4 \sqrt {c_1}}-\frac {\sqrt {c_1}\, t^{2} \left (i \sqrt {3}-1\right )}{\left (4+4 \sqrt {4 t^{6} c_1^{3}+1}\right )^{{1}/{3}}} \\ y &= \frac {4 i \sqrt {3}\, c_1 \,t^{2}+i \sqrt {3}\, \left (4+4 \sqrt {4 t^{6} c_1^{3}+1}\right )^{{2}/{3}}+4 t^{2} c_1 -\left (4+4 \sqrt {4 t^{6} c_1^{3}+1}\right )^{{2}/{3}}}{4 \left (4+4 \sqrt {4 t^{6} c_1^{3}+1}\right )^{{1}/{3}} \sqrt {c_1}} \\ \end{align*}

✓ Mathematica. Time used: 0.144 (sec). Leaf size: 42

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

\[ \text {Solve}\left [\int _1^{\frac {y(t)}{t}}\frac {K[1]^2+1}{K[1] \left (K[1]^2+3\right )}dK[1]=-\log (t)+c_1,y(t)\right ] \]

✗ Sympy

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

Timed Out