15.7.7 problem 7

Internal problem ID [2988]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 11, page 45
Problem number : 7
Date solved : Sunday, March 30, 2025 at 01:03:43 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} t x^{\prime }+x \left (1-x^{2} t^{4}\right )&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 34

ode:=t*diff(x(t),t)+x(t)*(1-x(t)^2*t^4) = 0; 
dsolve(ode,x(t), singsol=all);
 

\begin{align*} x &= \frac {1}{\sqrt {-t^{2}+c_1}\, t} \\ x &= -\frac {1}{\sqrt {-t^{2}+c_1}\, t} \\ \end{align*}

✓ Mathematica. Time used: 0.491 (sec). Leaf size: 48

ode=t*D[x[t],t]+x[t]*(1-x[t]^2*t^4)==0; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)\to -\frac {1}{\sqrt {-t^4+c_1 t^2}} \\ x(t)\to \frac {1}{\sqrt {-t^4+c_1 t^2}} \\ x(t)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.671 (sec). Leaf size: 29

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(t*Derivative(x(t), t) + (-t**4*x(t)**2 + 1)*x(t),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

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