63.4.27 problem 21

Internal problem ID [12991]
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 : 21
Date solved : Wednesday, March 05, 2025 at 08:56:26 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} x^{\prime }&=\frac {4 t^{2}+3 x^{2}}{2 t x} \end{align*}

✓ Maple. Time used: 0.016 (sec). Leaf size: 26

ode:=diff(x(t),t) = 1/2*(4*t^2+3*x(t)^2)/t/x(t); 
dsolve(ode,x(t), singsol=all);
 

\begin{align*} x \left (t \right ) &= \sqrt {c_{1} t -4}\, t \\ x \left (t \right ) &= -\sqrt {c_{1} t -4}\, t \\ \end{align*}

✓ Mathematica. Time used: 0.318 (sec). Leaf size: 34

ode=D[x[t],t]==(4*t^2+3*x[t]^2)/(2*t*x[t]); 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)\to -t \sqrt {-4+c_1 t} \\ x(t)\to t \sqrt {-4+c_1 t} \\ \end{align*}

✓ Sympy. Time used: 0.409 (sec). Leaf size: 26

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(Derivative(x(t), t) - (4*t**2 + 3*x(t)**2)/(2*t*x(t)),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\[ \left [ x{\left (t \right )} = - t \sqrt {C_{1} t - 4}, \ x{\left (t \right )} = t \sqrt {C_{1} t - 4}\right ] \]