Internal problem ID [3960]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 25
Problem number: 714.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational]
\[ \boxed {x \left (1-y^{4} x^{2}\right ) y^{\prime }+y=0} \]
✓ Solution by Maple
Time used: 0.141 (sec). Leaf size: 133
dsolve(x*(1-x^2*y(x)^4)*diff(y(x),x)+y(x) = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -\frac {\sqrt {2}\, \sqrt {x c_{1} \left (x -\sqrt {-4 c_{1}^{2}+x^{2}}\right )}}{2 c_{1} x} \\ y \left (x \right ) &= \frac {\sqrt {2}\, \sqrt {x c_{1} \left (x -\sqrt {-4 c_{1}^{2}+x^{2}}\right )}}{2 c_{1} x} \\ y \left (x \right ) &= -\frac {\sqrt {2}\, \sqrt {x c_{1} \left (x +\sqrt {-4 c_{1}^{2}+x^{2}}\right )}}{2 x c_{1}} \\ y \left (x \right ) &= \frac {\sqrt {2}\, \sqrt {x c_{1} \left (x +\sqrt {-4 c_{1}^{2}+x^{2}}\right )}}{2 x c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 13.903 (sec). Leaf size: 172
DSolve[x(1-x^2 y[x]^4)y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {c_1-\frac {\sqrt {x^2 \left (-1+c_1{}^2 x^2\right )}}{x^2}} \\ y(x)\to \sqrt {c_1-\frac {\sqrt {x^2 \left (-1+c_1{}^2 x^2\right )}}{x^2}} \\ y(x)\to -\sqrt {\frac {\sqrt {x^2 \left (-1+c_1{}^2 x^2\right )}}{x^2}+c_1} \\ y(x)\to \sqrt {\frac {\sqrt {x^2 \left (-1+c_1{}^2 x^2\right )}}{x^2}+c_1} \\ y(x)\to 0 \\ y(x)\to -\frac {1}{\sqrt [4]{-x^2}} \\ y(x)\to \frac {1}{\sqrt [4]{-x^2}} \\ \end{align*}