Internal problem ID [3887]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 23
Problem number: 640.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class D`], _rational]
\[ \boxed {x \left (y^{2}+x^{2}\right ) y^{\prime }-\left (x^{2}+x^{4}+y^{2}\right ) y=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 36
dsolve(x*(x^2+y(x)^2)*diff(y(x),x) = (x^2+x^4+y(x)^2)*y(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{\frac {x^{2}}{2}+c_{1}} x}{\sqrt {\frac {{\mathrm e}^{x^{2}+2 c_{1}}}{\operatorname {LambertW}\left ({\mathrm e}^{x^{2}+2 c_{1}}\right )}}} \]
✓ Solution by Mathematica
Time used: 5.133 (sec). Leaf size: 49
DSolve[x(x^2+y[x]^2)y'[x]==(x^2+x^4+y[x]^2)y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x \sqrt {W\left (e^{x^2+2 c_1}\right )} \\ y(x)\to x \sqrt {W\left (e^{x^2+2 c_1}\right )} \\ y(x)\to 0 \\ \end{align*}