Internal problem ID [3123]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 13
Problem number: 375.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Bernoulli]
Solve \begin {gather*} \boxed {x^{2} \left (1-x^{2}\right ) y^{\prime }-\left (x -3 y x^{3}\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 72
dsolve(x^2*(-x^2+1)*diff(y(x),x) = (x-3*x^3*y(x))*y(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {\sqrt {x^{2}-1}\, x}{\sqrt {x -1}\, \sqrt {x +1}\, c_{1} \sqrt {x^{2}-1}-3 \ln \left (x +\sqrt {x^{2}-1}\right ) x^{2}+3 \sqrt {x^{2}-1}\, x +3 \ln \left (x +\sqrt {x^{2}-1}\right )} \]
✓ Solution by Mathematica
Time used: 0.301 (sec). Leaf size: 53
DSolve[x^2(1-x^2)y'[x]==(x-3 x^3 y[x])y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x}{3 x+\sqrt {1-x^2} \left (-6 \text {ArcTan}\left (\frac {x}{\sqrt {1-x^2}-1}\right )+c_1\right )} \\ y(x)\to 0 \\ \end{align*}