90.5.5 problem 5

Internal problem ID [25124]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 1. First order differential equations. Exercises at page 71
Problem number : 5
Date solved : Thursday, October 02, 2025 at 11:51:06 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} y^{\prime }&=\frac {3 y^{2}-t^{2}}{2 y t} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 26

ode:=diff(y(t),t) = 1/2*(3*y(t)^2-t^2)/t/y(t); 
dsolve(ode,y(t), singsol=all);
 

\begin{align*} y &= \sqrt {c_1 t +1}\, t \\ y &= -\sqrt {c_1 t +1}\, t \\ \end{align*}

✓ Mathematica. Time used: 0.16 (sec). Leaf size: 34

ode=D[y[t],{t,1}] ==(3*y[t]^2-t^2)/(2*t*y[t]); 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to -t \sqrt {1+c_1 t}\\ y(t)&\to t \sqrt {1+c_1 t} \end{align*}

✓ Sympy. Time used: 0.237 (sec). Leaf size: 26

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(Derivative(y(t), t) - (-t**2 + 3*y(t)**2)/(2*t*y(t)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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