29.25.17 problem 714

Internal problem ID [5304]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 25
Problem number : 714
Date solved : Monday, January 27, 2025 at 11:07:57 AM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Solution by Maple

Time used: 0.193 (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 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}} \\ 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: 12.028 (sec). Leaf size: 172

DSolve[x(1-x^2 y[x]^4)D[y[x],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*}