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 : Monday, January 27, 2025 at 07:05:50 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Solution by Maple

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

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

\begin{align*} x \left (t \right ) &= \frac {1}{\sqrt {-t^{2}+c_{1}}\, t} \\ x \left (t \right ) &= -\frac {1}{\sqrt {-t^{2}+c_{1}}\, t} \\ \end{align*}

✓ Solution by Mathematica

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

DSolve[t*D[x[t],t]+x[t]*(1-x[t]^2*t^4)==0,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*}