Internal problem ID [3452]
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]
Solve \begin {gather*} \boxed {x \left (1-y^{4} x^{2}\right ) y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 129
dsolve(x*(1-x^2*y(x)^4)*diff(y(x),x)+y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\sqrt {-2 x c_{1} \left (-x +\sqrt {x^{2}-4 c_{1}^{2}}\right )}}{2 x c_{1}} \\ y \relax (x ) = \frac {\sqrt {-2 x c_{1} \left (-x +\sqrt {x^{2}-4 c_{1}^{2}}\right )}}{2 x c_{1}} \\ y \relax (x ) = -\frac {\sqrt {2}\, \sqrt {x c_{1} \left (x +\sqrt {x^{2}-4 c_{1}^{2}}\right )}}{2 x c_{1}} \\ y \relax (x ) = \frac {\sqrt {2}\, \sqrt {x c_{1} \left (x +\sqrt {x^{2}-4 c_{1}^{2}}\right )}}{2 x c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 9.514 (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*}