Internal problem ID [3421]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 24
Problem number: 682.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational]
Solve \begin {gather*} \boxed {\left (a -3 x^{2}-y^{2}\right ) y y^{\prime }+x \left (y^{2}-x^{2}+a \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 122
dsolve((a-3*x^2-y(x)^2)*y(x)*diff(y(x),x)+x*(a-x^2+y(x)^2) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\sqrt {-\LambertW \left (-\left (-2 x^{2}+a \right ) c_{1} {\mathrm e}^{2}\right ) \left (x^{2} \LambertW \left (-\left (-2 x^{2}+a \right ) c_{1} {\mathrm e}^{2}\right )-2 x^{2}+a \right )}}{\LambertW \left (-\left (-2 x^{2}+a \right ) c_{1} {\mathrm e}^{2}\right )} \\ y \relax (x ) = -\frac {\sqrt {-\LambertW \left (-\left (-2 x^{2}+a \right ) c_{1} {\mathrm e}^{2}\right ) \left (x^{2} \LambertW \left (-\left (-2 x^{2}+a \right ) c_{1} {\mathrm e}^{2}\right )-2 x^{2}+a \right )}}{\LambertW \left (-\left (-2 x^{2}+a \right ) c_{1} {\mathrm e}^{2}\right )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.389 (sec). Leaf size: 39
DSolve[(a-3 x^2-y[x]^2)y[x] y'[x]+x(a-x^2+y[x]^2)==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{2} \left (\frac {a+2 y(x)^2}{x^2+y(x)^2}+\log \left (x^2+y(x)^2\right )\right )=c_1,y(x)\right ] \]