Internal problem ID [3404]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 24
Problem number: 665.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational]
Solve \begin {gather*} \boxed {x \left (x y^{2}+1\right ) y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 137
dsolve(x*(1+x*y(x)^2)*diff(y(x),x)+y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\sqrt {-2 x c_{1} \left (-2 c_{1}-x +\sqrt {x^{2}+4 c_{1} x}\right )}}{2 x c_{1}} \\ y \relax (x ) = \frac {\sqrt {-2 x c_{1} \left (-2 c_{1}-x +\sqrt {x^{2}+4 c_{1} x}\right )}}{2 x c_{1}} \\ y \relax (x ) = -\frac {\sqrt {2}\, \sqrt {x c_{1} \left (2 c_{1}+x +\sqrt {x^{2}+4 c_{1} x}\right )}}{2 x c_{1}} \\ y \relax (x ) = \frac {\sqrt {2}\, \sqrt {x c_{1} \left (2 c_{1}+x +\sqrt {x^{2}+4 c_{1} x}\right )}}{2 x c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.293 (sec). Leaf size: 65
DSolve[x(1+x y[x]^2)y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (c_1-\frac {\sqrt {4+c_1{}^2 x}}{\sqrt {x}}\right ) \\ y(x)\to \frac {1}{2} \left (\frac {\sqrt {4+c_1{}^2 x}}{\sqrt {x}}+c_1\right ) \\ y(x)\to 0 \\ \end{align*}