Internal problem ID [2017]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _Bernoulli]
\[ \boxed {t x^{\prime }+x \left (1-x^{2} t^{4}\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (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: 0.37 (sec). Leaf size: 48
DSolve[t*x'[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*}