7.3.14 problem 16

Internal problem ID [2331]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 1.4. Page 24
Problem number : 16
Date solved : Tuesday, September 30, 2025 at 05:27:16 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

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

ode:=2*t*y(t)*diff(y(t),t) = 3*y(t)^2-t^2; 
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: 0.158 (sec). Leaf size: 34

ode=2*t*y[t]*D[y[t],t]==3*y[t]^2-t^2; 
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: 0.235 (sec). Leaf size: 26

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

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